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</div><h2>SL Paper 1</h2><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the following propositions.</span></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">p </span></em><span style="font-size: medium; font-family: times new roman,times;">:</span><em><span style="font-size: medium; font-family: times new roman,times;"> Students stay up late.</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">q </span></em><span style="font-size: medium; font-family: times new roman,times;">:</span><em><span style="font-size: medium; font-family: times new roman,times;"> Students fall asleep in class.</span></em></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the following compound proposition in symbolic form.</span></p>
<p><em><span>If students do not stay up late then they will not fall asleep in class.</span></em></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the following truth table.</span></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfgAAAC4CAIAAACAZWnwAAARKklEQVR4nO3dz2tbZ77H8fNvaCWDVjI23MGbSxfGK9OmYEwhmxnQwpnQhDAwK4OxcC8l0AGBQ8pAYUDYJHQ1CJdkM4SKQ2AYcEaiA52LbcFA2rr2Qgy+By2MCYfnLo5/SLJsf6bPic/3iPeLs0h/kCrvkT8+fixrAgcAGGtB1g8AAPB+MfQAMOYuhr5UnODi4uLiGrNreOgz+ESTT7TS0UpEKB2tROehGPpfglY6WokIpaOViKH3QisdrUSE0tFKxNB7oZWOViJC6WglYui90EpHKxGhdLQSMfReaKWjlYhQOlqJGHovtNLRSkQoHa1EDL0XWuloJSKUjlYiht4LrXS0EhFKRysRQ++FVjpaiQilo5WIofdCKx2tRITS0UrE0HuhlY5WIkLpaCVi6L3QSkcrEaF06beKD1qbj2vNbsq/beqisLbS2OvF4r/O0HuhlY5WIkLpUm4V7zdXPl1u7PTS/E3fk5OD7T9W5v+neXCi/NsMvRda6WglIpQu1VZHrdqvlxpv1Zvk7MW9nc2lpc0d4b6eofdCKx2tRITSpdgq3qvPz9f38jPzzjnnjvfqv56v79z4qBl6L7TS0UpEKF16rbrN5Q+UxbQm3qvPF1aa0Q0P3PTQv2uvzxQnSsWJmfW//dT+uvrhZKk4MX3vq78fSsdSt8BOq0R8+Ob56kKpODH94Otm/Tel8lp40zPg1lhrNUJ80NpcnguCoPDoz6/+OB/MLGfxTblUQ/VatbkgCIJgrra9d/qnC6Yq6389uHhexL3W+tzceuvyCUD8trE0532acXLQerY8VwiCqaU/v/zTfKGw3Iy8fsMLqbWKmsuFu/W940v/wEDA65+W8U59/oMbn6imh9455w637hcn79z7XfXp3w7juNf+8k5xcnFj18h6WWoV93af3y9PTN97vtt712t/eac4Ubq3dZj1wzpnqdUove/rlamgsFTfiVxvuzZXCIJPGwfvbv+BpB3q3UHj0yCYqywtr28fxO6oVfs4CIZG7ahVW5yrbQ9+E/Jkv/Go4HuaEe3UlwrBVKX+fe/0P12qNH70+R37pdQqjporhSvvizMNeOPTMt6pz5du/FrE+NDHUbg2XZy8s/7mtGAUVssTM+vtDD7+RjHUqvfmyYeTpQ+/bCe3FYdb9y19RnSmWo2QfPR+XGsdOeec+7FRKQUZndimHarbXJ7p+6PFUXOlEMzVWgOjFO83lgrn/45zLrnJHfw7/7G411qfCwpnC5gs5sgb518opVbHe/W7wZVDn2FA5WnZbS7P3PhFkvGh77XXP+o/f4g7G4uW9stMq6P2+iel4idP2mfPxXBtuvjRk7ah14ndbqvzr7ivcX5nNLRHyYdoUKq1MrmfSDnUu1atFPQNwfFe/e6otT3eq98tLDX2Tz+0jlq1j/v+sv83u17fDXtyB3pxptFtLs+km/XqVv/RE+Daoc8soPi07DaXZ268KbE99PHu5sLk9Gp4lviovf5Jqfz7b37mjH7Qu/aT/5ooLWx0Tv/H7oars6YO6J2dVol3rVrp/OM8GYXzD93kli2bA3qXdqh4rz5wqtvbrs0VLg/Q2T+aWWq8jU8n5hfcevdatY/Phz5ZyItThai5XAhSPKB3Pq0GngDXDX12AcWn5Rjc0R9u3S/OVsPkD5acQf/3w60f7KyXlVaHW/eL5ydascEDemenVWLg4/zHRqV0caeU6QG9SznUu4PGp30TFu3UlwqFR439kbdKJ/uNR4XCSvPof+vzpUsnzor+nTo92j474kj/gN6lNvTXnNFnGFB8WkqvF7I89Mn5Q7LsJ4dvvrpfnryz9u2hnZm30yoKq+WJ6QdbP8cnh282nqw/vl82dMCVsNIqMfBx3m0uzwSFR439k/jgr09rtS8qU1kd0LuUQ1380Vx8sL1eKQTzK80RN6On4p36fOmDuQ+u/s7k9fp3KrkDnVpqvI3jg+2ntdoXlUKqB/QutaG/5lU3GQbUnpb5f9VNr73+Uak4cXp9uLoZdgwdOTvnDLWKdjceTBcnSuXfPvm283/t9ZnibzY7aX5E+TPTyjk3fEPX29msFIIgmKrU/rJ3tF0rFTJ8SXWaoQaOhAtzy/Xm3vVf4idnDlO/9BWBA0c3p68YCYJCZf3V3n6rNpf6p8/Uhv6q++IsA0pPy/y/jn74gN4iK60GHHc2bL2CPmGy1QjDZ7K3LuWf9sz0z9L3UHbqqb6CPvG+fzLWTsArHskY/GRsFFbL5wf0RllpNeCnb+79yuAnSJOtLhs6k81AeqGuf3n47TpoVN7DYqb+XjeV+vd9xwZ2Ao5+Wsb7jaX5UT+odYnZoT/5eev308XffXNo5BXzo9lo1e/kMHx8p/ir+1s/Zf1IhtlrNUJ88GplrhBUGgfZPYbUQsVvG0tT2f5Zzh7JfnNl/n18f/s9vHvl3YutNxNw1NMy7u01liuP8/zulcmLBU9P503f1Gffql8UVsvn3cxtva1WIyQ/F3Mmuw/vVEINni1neE+afEv28kvX0/EenlTRXuOLWrNrJuAVT8sorK08a2kr74wOfX7QSkcrEaF0tBIx9F5opaOViFA6WokYei+00tFKRCgdrUQMvRda6WglIpSOViKG3gutdLQSEUpHKxFD74VWOlqJCKWjlYih90IrHa1EhNLRSsTQe6GVjlYiQuloJRo99FxcXFxcY3YND/0tf7bJL1rpaCUilI5WohJHNz5opaOViFA6WokYei+00tFKRCgdrUQMvRda6WglIpSOViKG3gutdLQSEUpHKxFD74VWOlqJCKWjlYih90IrHa1EhNLRSsTQe6GVjlYiQuloJWLovdBKRysRoXS0EjH0Xmilo5WIUDpaiRh6L7TS0UpEKB2tRAy9F1rpaCUilI5WIsNDH4XV8tVv0LOw0cnq/5a9j41WcRSuTV/5TkaTixu7BlIZaZUDhNLRSmR66D978Hy3Fye/rpYnplfDyDnn4l5nq/rgOUN/Jo7CPzzc+Gfv9Ndr08XZath1zjkXdbY+f8jQ5wqhdLQS2R36uPPqZef49C8Ght45d9x58YqhP9NfY2jonYs7L19YSGWkVQ4QSkcrkd2hHzA89FbYa3Vp6M2w18ooQuloJWLovdhrxdDnHqF0tBIx9F7stWLoc49QOlqJGHov9lox9LlHKB2tRAy9F3utGPrcI5SOViKG3ou9Vgx97hFKRysRQ+/FXiuGPvcIpaOViKH3Yq8VQ597hNLRSmR/6Lvh6mzfD/TbmjBbrYbeNKK8FkYWflLqlK1WhhFKRyuR/aE3jVY6WokIpaOViKH3QisdrUSE0tFKxNB7oZWOViJC6WglYui90EpHKxGhdLQSMfReaKWjlYhQOlqJGHovtNLRSkQoHa1EDL0XWuloJSKUjlYiht4LrXS0EhFKRysRQ++FVjpaiQilo5WIofdCKx2tRITS0Uo0eui5uLi4uMbsGh76W/5sk1+00tFKRCgdrUQljm580EpHKxGhdLQSMfReaKWjlYhQOlqJGHovtNLRSkQoHa1EDL0XWuloJSKUjlYiht4LrXS0EhFKRysRQ++FVjpaiQilo5WIofdCKx2tRITS0UrE0HuhlY5WIkLpaCVi6L3QSkcrEaF0tBIx9F5opaOViFA6WokMD30UVstXv2/DwkYnzvoRWmkVR+Ha9OhQk4sbuwY6OWelVQ4QSkcrkemh/+zB891enPy6Wp6YXg0j55yLe52t6oPnDP2gbrg6WyqvhdF5l5PD8PHiabTsWWplGqF0tBLZHfq48+pl5/j0LwaG3jl33HnxiqEfdHnonYt3nz99zdDnC6F0tBLZHfoBw0NvhaVWw0Mf/+u7f0QGPhmesdTKNELpaCVi6L1YajU09Eftp1+FDH0OEUpHKxFD78VSq264OjvwndihY5ysWWplGqF0tBIx9F4stRq6o492n339mqHPIULpaCVi6L1YasUZ/ZgglI5WIobei6VWo151Y4mlVqYRSkcrEUPvxVIrhn5MEEpHKxFD78VSK4Z+TBBKRyuR/aEfejHJbDXsZv2QLthoNfwWCAY/IzorrXKAUDpaiewPvWm00tFKRCgdrUQMvRda6WglIpSOViKG3gutdLQSEUpHKxFD74VWOlqJCKWjlYih90IrHa1EhNLRSsTQe6GVjlYiQuloJWLovdBKRysRoXS0EjH0Xmilo5WIUDpaiRh6L7TS0UpEKB2tRAy9F1rpaCUilI5WIobeC610tBIRSkcr0eih5+Li4uIas2t46G/5s01+0UpHKxGhdLQSlTi68UErHa1EhNLRSsTQe6GVjlYiQuloJWLovdBKRysRoXS0EjH0Xmilo5WIUDpaiRh6L7TS0UpEKB2tRAy9F1rpaCUilI5WIobeC610tBIRSkcrEUPvhVY6WokIpaOViKH3QisdrUSE0tFKxNB7oZWOViJC6WglMjz0UVgtX/GmDQsbnTjrh+ecs9IqjsK16Svf4GJycWPXQi0brXKAUDpaiQwPvXNnEzZbDbsXf+vw288WPg8jC9tlpFUchX94uPHP3umv+4tFna3PHzL0uUIoHa1E+Rt65447z+oMfZ/jzotXZ1/iXCoWd16+MPH1j41WOUAoHa1EeRv6+If2d//O9CENsNQqMfJTown2WhlFKB2tRPka+rjXrj+xNGGWWiUY+twjlI5WolwMff+3Fm1NmKVWCYY+9wilo5UoF0Pfd0e/29h8bWjCLLVKMPS5RygdrUT5GnrO6G/E0OceoXS0EuVt6I2x1Cpht5i9VkYRSkcrEUPvxVKrhN1i9loZRSgdrUQMvRdLrRJ2i9lrZRShdLQSGR76obdAKK8Z+SGpflZaJWwXs9XKMELpaCUyPPR5QCsdrUSE0tFKxNB7oZWOViJC6WglYui90EpHKxGhdLQSMfReaKWjlYhQOlqJGHovtNLRSkQoHa1EDL0XWuloJSKUjlYiht4LrXS0EhFKRysRQ++FVjpaiQilo5WIofdCKx2tRITS0UrE0HuhlY5WIkLpaCUaPfRcXFxcXGN2DQ/9LX+2yS9a6WglIpSOVqISRzc+aKWjlYhQOlqJGHovtNLRSkQoHa1EDL0XWuloJSKUjlYiht4LrXS0EhFKRysRQ++FVjpaiQilo5WIofdCKx2tRITS0UrE0HuhlY5WIkLpaCVi6L3QSkcrEaF0tBIx9F5opaOViFA6WokYei+00tFKRCgdrUQMvRda6WglIpSOViLDQx+F1fIV786zsNGJs354zjkrreIoXJse/TZGk4sbuzZSGWmVA4TS0UpkeOidO5uw2WrYvfhbh99+tvB5GJmYL0utuuHqbKm81lfm5DB8vLgaRlk+qguWWplGKB2tRPkbeueOO8/qDP0ll4feuXj3+dPXDH2+EEpHK1Hehj7+of3dvzN9SAMstRoe+vhf3/3DxqfDhKVWphFKRytRvoY+7rXrTwbu7jNmqdXQ0B+1n35l5OuehKVWphFKRytRLoa+/7uLQ8c4GbPUqhuuzg58J3boGCdrllqZRigdrUS5GPq+O/rdxuZrhn6koTv6aPfZ168Z+hwilI5WonwNPWf01+CMfkwQSkcrUd6G3hhLrUa96sYSS61MI5SOViKG3oulVgz9mCCUjlYiht6LpVYM/ZgglI5WIsNDP/QWCCYnzEar4dcmTZv5adh+NlrlAKF0tBIZHvo8oJWOViJC6WglYui90EpHKxGhdLQSMfReaKWjlYhQOlqJGHovtNLRSkQoHa1EDL0XWuloJSKUjlYiht4LrXS0EhFKRysRQ++FVjpaiQilo5WIofdCKx2tRITS0UrE0HuhlY5WIkLpaCVi6L3QSkcrEaF0tBKNHnouLi4urjG7BoYeADCWGHoAGHMMPQCMuf8H706V/rE+34sAAAAASUVORK5CYII=" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down a reason why the statement \(\neg ( p \vee \neg q)\) is not a contradiction.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the statement <em>\(p \Rightarrow q\)</em>.</p>
<p class="p1" style="text-align: center;">If I break my arm, then it will hurt.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down in words, the inverse of <em>\(p \Rightarrow q\)</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the following truth table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-03_om_07.18.13.png" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State whether the converse and the inverse of an implication are logically equivalent.</p>
<p class="p1">Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">For events <em>A</em> and <em>B</em>, the probabilities are \({\text{P}}(A) = \frac{4}{13}\) and \({\text{P}}(B) = \frac{5}{13}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If events <em>A</em> and <em>B</em> are mutually exclusive, write down the value of \({\text{P}} (A\cap B)\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If events <em>A</em> and <em>B</em> are independent, find the value of \({\text{P}} (A\cap B)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If \({\text{P}} (A \cup B) = \frac{7}{13}\), find the value of \({\text{P}} (A \cap B)\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The universal set <em>U</em> is the set of integers from 1 to 20 inclusive.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>A</em> and <em>B</em> are subsets of <em>U</em> where:</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>A</em> is the set of even numbers between 7 and 17.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>B</em> is the set of multiples of 3.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of the following sets:</span></p>
<p><span><em>A</em>,</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of the following sets:</span></p>
<p><span><em>B</em>,</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of the following sets:</span></p>
<p><span>\(A \cup B\) ,</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of the following sets:</span></p>
<p><span>\(A \cap B'\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Dune Canyon High School organizes its <strong>school year </strong>into three trimesters: fall/autumn (\(F\)), winter (\(W\)) and spring (\(S\)). The school offers a variety of sporting activities during and outside the school year.</p>
<p>The activities offered by the school are summarized in the following Venn diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_10.56.10.png" alt="M17/5/MATSD/SP1/ENG/TZ1/04"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of sporting activities offered by the school during its <strong>school year</strong>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine whether rock-climbing is offered by the school in the fall/autumn trimester.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the elements of the set \(F \cap W’\);</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down \(n(W \cap S)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, in terms of \(F\), \(W\) and \(S\), an expression for the set which contains only archery, baseball, kayaking and surfing.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(p\) and \(q\) represent the propositions</span></p>
<p style="text-align: left; margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(p\): food may be taken into the cinema</span></p>
<p style="text-align: left; margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(q\): drinks may be taken into the cinema</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table below for the symbolic statement \(\neg (p \vee q)\) .</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down in words the meaning of the symbolic statement \(\neg (p \vee q)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in symbolic form the compound statement:</span></p>
<p><span>“no food and no drinks may be taken into the cinema”.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the three propositions <em>p</em>, <em>q </em>and <em>r</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> p</em>: <em>The food is well cooked</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> q</em>: <em>The drinks are chilled</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> r</em>: <em>Dinner is spoilt</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the following compound proposition in words.</span></p>
<p><span>\[(p \wedge q) \Rightarrow \neg r\]</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the following truth table.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-20_om_07.32.41.png" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the following propositions:</p>
<p>\(p:\) The lesson is cancelled</p>
<p>\(q:\) The teacher is absent</p>
<p>\(r:\) The students are in the library.</p>
<p>Write, in words, the compound proposition \(q \Rightarrow (p \wedge r).\)</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the following truth table.</p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Hence</strong>, justify why \(q \Rightarrow \neg r\) is not a tautology.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">You may choose from three courses on a lunchtime menu at a restaurant.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>s</em>: you choose a salad,</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>m</em>: you choose a meat dish (main course),</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>d</em>: you choose a dessert.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">You choose a <strong>two</strong> course meal which <strong>must</strong> include a main course and either a salad or a dessert, but not both.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the sentence above using logic symbols.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in words \(s \Rightarrow \neg d\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the following truth table.</span></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoIAAACWCAIAAADFSn7mAAAN5klEQVR4nO3d32tb5x3Hcf0BvdmlL4YDpjCH+KKEQdiFcaGYrgFhCrmZwYSEUodetFcuwZ5bvO5mBo+ZwGAgJJINSoexSQgbIdrBo4SEydtK29k6LFB3sUUQWXY4DM2kT55dyL90JNtp/eNIn+/7xXOTQhrBO9HHRzqyMx4AAKQk473v6T7F4XA4HA7nJA8zzOFwOBxOaic5wyldjuNQaCeMuPJIbBYzrIN2wogrj8RmMcM6aCeMuPJIbBYzrIN2wogrj8RmMcM6aCeMuPJIbBYzrIN2wogrj8RmMcM6aCeMuPJIbBYzrIN2wogrj8RmMcM6aCeMuPJIbBYzrMNoO7dSyJ7u6T7Vk82HLu0Hc2yMxrWExGYxwzoMt6sG468N5Vd0V9hyXCtIfCJq5dyFTCaTyVxI+5HsYIZ12G0XBRO9/RNBNe3HcYzsxjWDxCfFRcWrXYO5tB/GDmZYh9l2LswP9U4GkfDFsN24dpD4pFSLY2e7xoppP4wdzLAOq+1qYX64bzyI0n4cx8pqXENI/GK+ib9YyP/pX8++8//ALecGfzRWbKMXzwzNsKvcm718rqf73Fu/uleJlm7Mq93QI9yuSRQG+YnXT/f0jhb+cb+QfUX7jWFvK65RJH4xtdW5d19++a3cF/95/p1+vyvnBruuFtvpxTM7M1wNxvv7RufXnHeVux+8/preW4m67Rq5tWAy23f513+pbHi3FsyMvtE7XAhraT+s42Ul7kHc+qczI2cymTMjM5+uR6XCXLmNnk0PRzrxxvqDayNdmUzXyMyDR1Hp93PlQ/yDfV699/Pz33v1Z3fX//div8HF5WJubDCTOTOSe1DKXcgM5trq742ZGXYrhezprZcua2F+Su+JW7Zdg6dLM2/2Xb6xEtf/GdXC/LD2R5XqbMQ9ULU4drbr0twj5936nasD7fXS4iEpJ46KY11nLs195fzGevHDgT0uRp+Vpnsy38JLr/7i3r+/OejPrv+JIzMP1p3fWC/OjAycGcwtt9UThpkZ9i5emn2jO/tBsNZWAY6Qbrtt9Yi7r31rYf6i/CvS3kTcF+CWc4NdXWPF+hfT5dxPc4e5qGozwoldOTeYObv5NZNbzr1dOPzF6PP4s9zFsy9fLHwR77PELi7NDHRdyi1Hux7JhXb7a2Nnhr33G2vz7/V1v/nLpadpP5JjId3Oe++9W10YPddwN5aBjyrVKcR98Yudkbn11v8LF5dmBjKDV4uP9L7watfEcWl64MWyvT23vteNU09L0+czAx8W1zeO7oE9f7b+h/d/2LXfEscPpgd6dl/7unJusM1ekfbGZtjXX9LseX12KW6zDkdBvV3z6D5dmnmzR/2jSnUKcZ/HX39WOsifr797du8Z9t5vPJp7pytzfrqk9sV0uyb+Jv768wOz3b/+7vf3m2Hv3Vdzl85kBmZKR/bcuz3Dvy3XWt6ttfFo7p2uhhfANz+q1G6fqrAwwy4Kcje2XsZ0YX6oW/OOHsV2DVyYH+renuGNytLtwnhW/qNKdfJxt8Sl6YF9Z9hvXVod4RN6W+joxM9K0z37z7DfvDYdmH4QH8Wf+AIvSidGt/5Sytk2vJ/AwgzXwvzFNybvVpz3PlrJj/ZxNdyhomCi99yV+VXno/Dm7xbqH1XK3V36W0UwZyP9uJv2mmEXFX9T2HpLrz3f4Tukjk689wxXizMfb70IXCvve5fyt7xF66UD3hhuuJPAu/XSQm5sr7vD0mVhhp/8fWn12eaHhk/1XZ4thpqXT4rtEqKV/GjfdkS3Usi+svUFljgDcev2muFaOfeTgat31p33PlrOXeriarid7DnDbjk3eH7zvfz489zI2cNfDT+Pl+fe//EPDrg5y++6r97F5du5uVIpdyEzeK1Y+ny9zf7iWJhhK2gnzEzcvWb4yV9LXz3b/NBwpmtk5k5Z7Yvpjk685wxHX5b+GW1+aDhzZmT6j+XDfvH033Lu4qvvffzlARvsvXfxcqH+YeXpO+W4fi1+xLeJHQ1mWAfthBFXHonNYoZ10E4YceWR2CxmWAfthBFXHonNYoZ10E4YceWR2CxmWAfthBFXHonNYoZ10E4YceWR2CxmWAfthBFXHonNYoZ10E4YceWR2KzWM8zhcDgcDufEDjPM4XA4HE5qJznDKVyW49BoJ4y48khsFjOsg3bCiCuPxGYxwzpoJ4y48khsFjOsg3bCiCuPxGYxwzpoJ4y48khsFjOsg3bCiCuPxGYxwzpoJ4y48khslvYMuyiY7Nv3o1p940GU9qM8KlrtmkTBRO++H7zrnQwil/ajPC7icUFiw+RneGpo8m6l/uTsVgrZ07uerKNwfnKIGe4UUTCR/SiobHjvva+F+eGe7v6JoOq9997F4fxEdooZRucisVnqM7x4e3H7qTk5w9776uL8fWa4M0T3FxarW79IzLBPtpYjHhckNkx8huOHDyvbz8wtZnjjceWJzDO3Vrsm8Wq4eSnsW82wd48rj2VaNhGPCxIbpj3DjVrMsBTldkktZlibpbhGkdgsZliHcrskZhhqSGwWM6xDuV0SMww1JDaLGdah3C6JGYYaEpvFDOtQbpfEDEMNic1ihnUot0tihqGGxGYxwzqU2yUxw1BDYrOYYR3K7ZKYYaghsVlGZrgajPc3fP/hbD6U22LRdgnN3yd8uBDW0n5Ux85GXNNIbJaRGTaBdsKIK4/EZjHDOmgnjLjySGwWM6yDdsKIK4/EZjHDOmgnjLjySGwWM6yDdsKIK4/EZjHDOmgnjLjySGxW6xnmcDgcDodzYocZ5nA4HA4ntZOc4RQuy3FotBNGXHkkNosZ1kE7YcSVR2KzmGEdtBNGXHkkNosZ1kE7YcSVR2KzmGEdtBNGXHkkNosZ1kE7YcSVR2KzmGEdtBNGXHkkNkt7hpt/Nm3y9I0HUdqP8qhotWvW9EOjG474Tx1WjwsS2yU/w1NDk3crrv6rlUL2dE/vZBDVfx2F85NDzHBncasLo+d2RfTeex+vLIxfnAiq6T2sY2cirm0kNkt9hhdvL24/Xydn2HtfXZy/zwx3lGow3p+cYe9d+MksM4xORmKzxGc4fviwsv103WKGNx5XnrjWv7fzaLXbS+sZlmcjrmkkNkt7hhu1mGEpyu12NM2wC2/dDDWL7mIjrmkkNosZ1qHcbkdihl28dO1KfkWz6C424ppGYrOYYR3K7XY03y99eogZRucjsVnMsA7ldjuSL0q7tZtT15lhdDwSm8UM61But4P3hqGJxGYxwzqU2+3gTmloIrFZzLAO5XY7mGFoIrFZzLAO5XbbWn4XLQNMxLWNxGYZmeGm22uzeb23E0XbbWuKaGmM1eOCxHYZmWETaCeMuPJIbBYzrIN2wogrj8RmMcM6aCeMuPJIbBYzrIN2wogrj8RmMcM6aCeMuPJIbFbrGeZwOBwOh3NihxnmcDgcDie1k5zhFC7LcWi0E0ZceSQ2ixnWQTthxJVHYrOYYR20E0ZceSQ2ixnWQTthxJVHYrOYYR20E0ZceSQ2ixnWQTthxJVHYrOYYR20E0ZceSQ2S32Go2Cid++Pamn9uEO1dgn7p+wW/7mH4nFBYsPUZ9h7771bm7/Se6pvPIh2/bc4nJ/ITik9cUu22xEFE9mPgsqG9977Wpgf7ununwiq3nvJmgnicUFiw0zMcP1CqnGGvfe18HpO6Ylbs9226P7CYnXrF4kZ9t67aPH2olDNBPG4ILFhlmdYjWa7bfFquHkp7FvNsHePK49lV1g9LkhsmNEZduGdW2EtzYd0DDTbtdZihrVZimsUic2yOcNPl2bGC8xwB2OGoYbEZhma4cYba4eZ4U7GDEMNic0yNMO7roY31uZnbzDDHYwZhhoSm2VzhnlvuNMxw1BDYrOMzrAkzXatMcNQQ2KzmGEdmu1aY4ahhsRmmZjhVt9FS5Bkuz0ww1BDYrPUZ7jpHmnhMVZr15qLgsk+9Zvem9mIaxqJzVKfYUtoJ4y48khsFjOsg3bCiCuPxGYxwzpoJ4y48khsFjOsg3bCiCuPxGYxwzpoJ4y48khsFjOsg3bCiCuPxGa1nmEOh8PhcDgndphhDofD4XBSO8kZTuGyHIdGO2HElUdis5hhHbQTRlx5JDaLGdZBO2HElUdis5hhHbQTRlx5JDaLGdZBO2HElUdis5hhHbQTRlx5JDZLfYabftBhw8nmQ5f2Izw6au2SqsF4/963+4v/uEP1uCCxXeoz7L333q3NX+lN/KRhF4fzE9mpINLZYcl2SW51YfRcT+9kQ7h4ZWH84kRQTe9hHTsTcW0jsVkmZrh+Tdw4w977Wng9xwx3mmow3p+cYe9d+MksM4xORmKzLM+wGs12Sa1nWJ6NuKaR2CyjM+zCO7fk3krUbJfUNMMuvHVT6S3+1mzENY3EZtmc4adLM+N6d/RotktKzLCLl65dya8ww+h0JDbL0AzL31ir2S6p+X7p00PMMDofic0yNMO7roY31uZnbzDDHSn5orRbuzl1nRlGxyOxWTZnmPeGOxfvDUMTic0yOsOSNNslcac0NJHYLGZYh2a7JGYYmkhslokZbvVdtARJtktq+V20DDAR1zYSm6U+w033SAuPsVq7pKZ7pC2NsXpckNgu9Rm2hHbCiCuPxGYxwzpoJ4y48khsFjOsg3bCiCuPxGYxwzpoJ4y48khsFjOsg3bCiCuPxGYxwzpoJ4y48khsVusZ5nA4HA6Hc2KHGeZwOBwOJ7WzM8MAACAVzDAAAKlhhgEASM3/AQuCIZ6+mbTwAAAAAElFTkSuQmCC" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;"> A group of 33 people was asked about the passports they have. 21 have Australian passports, 15 have British passports and 3 have neither</span>.</p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A group of 33 people was asked about the passports they have. 21 have Australian passports, 15 have British passports and 3 have neither.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number that have both Australian and British passports.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>In the Venn diagram below, set <em>A</em> represents the people in the group with Australian passports and set <em>B</em> those with British passports.</span></p>
<p><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUwAAADUCAIAAAB4To2SAAAXiElEQVR4nO2d/3MUZZrA+U96ahpSQumhsJQUp0zFQlRKKKS0b5TyK4swqQN3XWCtHvAuYU/pcSX+sGTu4l7FukncOqSqx60KV6a9jbfGXrAYr6FMStu9uEIbi+QaL4k0gQn93g9P0mYHkkyS7n6/9POp+YUhM/3O9Pt5n+d93rd7lhEyMWJblR/57MKlcZ8QQgipjtjB0z8+iyAITywjZGL4/Icnjz1zh5SS17zYerLn7MVA8ssXet4+mLmz8UBHb+XiTMllKYUPfOCDi8cyQggh/tW+o6ulVdvaP79RMwj4f+76u/3vXbxe87QspSIbdxAECY1Acm+gXZElpX3Aq/kLf7j7Z8+fvHhLoo6SIwgXTEt+84t3tq2SN524cL3G5pujvS2Pd3xx83avjKWFCIIsiSnJ/cGurCRvOHbmau0fXOlrzt0a3glKjiCcAJJXh/T9DdLGw70jtf8/ca5161uVidtU1VFyBOECWUotI/63p/etl1e+2jtak5X718+feLS575bwPvXKOBqIIMjSkKXUMjLae3hl6o593cO1AfvqQHvuNuF9+pXRNw9BkKUiS6ll5Dt9t7Tiofb+yZr/9M61PtR8S3j/8ZXRNw9BkKUiS6llZLh7f3rV9toSenW458hDzR+Pzf7K6JuHIMhSgTn5yBltR0OmuWdoYvr5ieFz/7rngYPli9fmeGU8TUQQZClML6GNf/F+y5Nr0xuVl1uOv9nyiycy657QTg+OzbFXHSVHEC4IdrwRQvzqyFeVPuN075l6LkVByRGEC2ZKvuBXhtsUBEGiACVHEMFByRFEcFByBBEclBxBBAclRxDBQckRRHBQcgQRHJQcQQQHJUcQwUHJEURwUHIEERyUHEEEByVHEMFByRFEcFByBBEclBxBBAclRxDBQcnjxvM827Zt27Ysq6zrczzgzxzHod3kkHEcBz6aYRhzfHzLsuDPPO82v9KF1A9KHi2O45imWdb1vKo25XLwY9FNuVxeVfOq2lkqzdbFi21F+JusosCr8qpabCuC/K7r0v5kdQEjWvBxGjMZWUo1ZjLw0eDjzPaAv6n50sq6bpqmeANfpKDk4QPdOq+qQYeGrrmUoOS6LoS+zlIJ3jmrKAVNMwyDtR7vOI5hGMW2IgxPTblcKGOTbdvBcAnvDKOkZVkY6ucGJQ8H13UNwyhoGujXWSqZphlpvAWXCprWmMk0ZjLFtiLd7m5ZFojdmMnA6GPbdnSHc13XsqzOUglCfV5VDcPgJcGJGZR8SYDb0M8Kmha12LPhOE5Z12c2I7ZDg9uNmUxTLtdZKkUq9mx4nmeaJox3WUUp6zraPhOUfJGYpglpM0jFSMYYDDoQ26PL5F3X7SyVGJQKBh2YJrBzXuiCki8M13XLug6d2zAMZvuQ4zhBgA03sMPoFvUgskQgtsNg11kqsTMGUQElrxfXdSFEFDSNSlK6CKCvZxUF4u0Sh6TgrVge3WqwbRvOWrGtmFjVUfL5CfTmt6NYlgXhd3GqB3rHOdsPEQHO4FJAyefC8zyROodt26B6/a7yrvdMEqs6Sj4rMPfOq6pgHQK8bcrl5p50wIgght4zAdUXndTwiLCS++ODF/7yw+Jea9s2hC9e5t6LAIawgqbd2tE9z+sslWQpJbAGtm035XKhnGJ//NKFSsBn9fwicMwIKrn/Xe+RHbv1Swt9HfRvGOajaBdTuK4La8szY7VlWULmL7fFMIzZRrq68asjX36i/+rxdEpes/Pwm2+0vJzNpNcpLb+3xyfDbOsSEFLyiaFu9V5ps3ZmdEEvgwCekP4dAFYXNC1w3jAM2o2Kj+BTW5a1+HcZ7t6fTt2V7x0lhJBJt0e9S1qx6fg5RrIg8ST3bwye3LtGlqVHWivj9b+srOuylEpU/w7wPA92y2UVJVEDXIBpmrCivqiQfnO099W7pA0Hey5PPfGdvltKyds67JuhtnKxCCf5tQvtz+07mLtPlvaVv6vW8wro4k25HLNbO6LGMAyoOUNHp90cOriuu9hu8P3ZY4/I6f3lIehvU5G88difFhBkokQsyf0rlbcOFc58+XHzA3L65dPD80+KbNuGzVuiVpjmxvO8gqZlFQV6tuM4cEVnMr8NQghUZBaWul+3TmxaIStdX/uEkInhStehh1eve7HUj3PyCKgO977+fOunY/6l8q575LuPV+YL5KZpJjZFJ9Oxq0bpGu0TCKTu9Vdeb9od26VUw/2P7Xx4rSyl5PRjLd1fMVVhF0ZyvzrU/cre0pfXfDLZ3/7gCvnB9oE5R1LITgVeJJsbx3Eghbnt/0JAwy+njr+d+LrreVlS2gc8QibHBz9s3bm2YcvrvUMTkbeybkSR/MZX7+3ZuPbhp3bv+unuF3Zk0il5l/7d7H8OVz4nPFjNncJAmiPYTpj6gUrN/DMXf/C9Z++RN7RWJiB2+1f7jq6W5HubPx6LpZ31IIbk4192HHql+5up9Pyv1jNq8TwPbiqU2Gln/fbC6lrCPZ+7q/jD3S8tT61u7rs6/Uy1cnytNE+MiRkBJJ8cO/eb54/+8cr0LMi/dPJZKbX2dlPyek6b2EAMr7+wBIlrkj0vaNrsHQYWzzYe7h2Zfuaq3fFcg7T6ya6v2Fg+I4R/yf3q0AdHHjzc4wbzb3/ijHaPtOKh9v6aKTkaDoYvdJKScM8JIcW24izdZqQ3v1FefuD0cJUQQvxRW/+HR9MyU6V1wrfk/vD5U7/ek1klL8+26J//n0+IP3zhdEl7ZoMspRoePth+6sylG1PxHQ1fnOEAen6L55Pj9n+d+peDW9IpOb3x8Rd+unvXU1vulhvuf7a546OvWTKc8C35Qph9ME4ElmUtsYqGnvMbJBIhecIND8tPGCkSu64GyWB962psIb7kcKVRMrdkE0Jc1w3xmpOl5PwC4Hke3G+bdkMWhuCSwyJQkjtl6MGns1TKKgqmRbQbsgBElpzH8xEusPwTxdvmVTX0t+UF27ZlKcVR5BBWcghi3GVWIQLzlChCLn63ZV3nKJ0RVnIottFuBTUcx4m0SAZZ0pJutMA5BU0raBrtVtSFmJLDVDyxxTaoD0V9BysowvESzUIHvmQuLmEUUHKoJyc5yMAvn8ZwII6iWRTAzQjYn5wLKHleVbHnxZPFeJ6XtHvC1QA/q0q7FfMgmuSQqGMOGdsR8QuPYWa0RISSHAILJuoxHxSTdsYLQEJJTqWLswNU1OPvbVAESex2V0JIsa3I8jAnjuS0ujg75FWVVt4I68ZUDs0CkEIyO8yJIznFLs4C1OfG4v1q2oJgeZgTRHKYFyW2/EMYcIz6KEMd6qdgNgSRPOFhHH6olHYr8CwwcRZuRQTJLcviaCNxFDASQzCfYuRE1CCC5BhA2AkgeC7YORcB3EuO0YOp6AG/DEu7FTRh6nQA3Eue8NDBoFQM9vI4MU2TtY2ufEvuuq4spZIcxhkc4xjs5XHC4Jo535J3lko83lgvLNgc46CXs39tVnSw1i35lpy1ITNmWOtMAcw2LB5YG3w5lpzNSmacZBWFzatx4L4x7PTy+MmrKjuFCY4lL2hakq9kht0BtFsxK025HDu9PH6YKkzwKrnneQm/HKXYVmT5VoqGYbB8YVbUMNU/eZWcqZGSCowXt1ibl8YPO5kmr5Kz8w1SgcHl8VvBjJ2ROMSr5IzfiyNqOksllnN1oKzrSa6xQ8bOQi7DpeRcxLFIacrl2KyrzwRq7LRbQRNGchkuJecijkUHTHdpt6IuGC8cRA0juQyXkudVlf04Fh2mafJyKzssnbCQcnIpOSNTHVp0lkqs7VefjYQvpBFCWFhI409yRkZHijTlcrxs5sVpOQtZJ3+SG4bBwjyHInwlMiyEMoqwkHbxJ3mxrYjTPNqtWAAshDKKWJZFvYDCn+QcJatRwN0sl4VQRhEWJiz8Sc5Xsho6ZV3nyxnuRqXQod5jOZMcfpEn/uOyA3fZr23b1PNVulDPPTmTnMUe4w2UtX1b0il5/WsffHry1V1P7bh/VUPmkD4YyeAdfo+pXq6827Jn3687S2/88rWjv1i/avNvrOvhvX08W3f8K5XfvXng8eUpedOJCxPf93e93Jhet797KOrj1gP1a8s5k5zR3K9aab07Jf/tk0f+7dPhqu+7PYdWyhuOnbkawaFC/tqrTm/Ljg0Hu4eqPiHX7I6dsvSIdub7MA8RW1epVlrvlu87/ocL77529M1DW6TtrZXROI47H9RnWJxJTv37ui037Y7tknzvoQ+GfULIlPMNf989HMGxQv3avf/p2nPHT5p7r0wSQggZPXtss7zy1d7Rm+EdghBCsooSQ77qD3ZlpQ1N/3j0n94frPrjzl/+txr1IeujrOt0d2FzJjmTpdrrF0/ubUg/986XU5HbH9L3pFc81N4/GfaRbNsO8epFf0jfu3x1tmPgBvz7unVi04o7DvRcCesA0+RVNXrJq0P6/gZp9aYjxtRQywzUV9E4k5zFspP/7el962Wl6+upvlUd7j5wxwznQyTUksT1iyf3NkjPdw1OEEIImbzS23yvtP6l7m9DdyQWyS/3HNggL3+pPHQj4gMtGOqFJP4kZ26RfLT38MpV2zu+mMpxr11of2L9ttZPxyKIJ6F2lyt9zQ/If6OdnfAJIf7wf76aWSGn9753McSi2xRx5F+jvYdXrth0/ByDi6so+cJgT3L/at/R1dKOE+fHCSHE//78iWfufbHUPx56qk4IIaZphld3HKsc3yqnX+wa/GF8sOetI0ebX1gnb+uwQ56PExJHJcW/eqawITgLjEF93RclXyJjleNbZWnD082/fU//9/YDTyqHTw1EYzgJ2Rb/Wv9vlXRKluR1u/75zJ+NljsjqSOQOCQfqxzfKt95tO8qY9Pxaehe/8+Z5NT3FdRy3TqxacXq5o8uX+qvVCx7ZCLSo4Vty+T4pf7KhUvjvn/9/InN0tbWylh4b/4jbK6JxAlKzvpB5+Cm3bFd2ni4dySew0VmyzW7Y2d0kRAlR8lZP+jsXLM7dsrp/eWhmFZko7LlxuftW1dFsXgGoOQo+QJg6J5h3kC5VX16jSynt+x//e2eaDax1hCBLWMD+gntwBNrpVTDw/sK+kAUHwMlR8kXAHuFt1jh1BZOmx0iKPkCQMl5vCtOwiWHG7BTbABKzhPUt1UsjoRLHu5m5EWAkvMEp5JTv9aSLtTPGmeS4w3eOJUch2aKDeBM8oQnfhz9dspMmNvCFC/U7y/Mn+RJ/oEkQrtOuzio3+SMLtQjE2eSU898qMPQToG64XFgChHqvxXFn+R83XU8dLib31KvLVOH+injTHKKx2WEYluRr6oERz/PGBGNmQzd35DhT/J4bhjGLNzth6E+I6UL9Z0whEfJcdGVr8CI54v6+eJP8oQX2FmIDAsiqyjcVQpDhIXMiz/Jqd/7kjocacPpwn6IUC+tEx4lx37DQr+pExyRWVjy5E9ykvjaG6M/I3M7mLxPfnxQv4UjwKXk3C0jhQsLv4ZbJ025HHP3yY+RUO+uu3i4lByXXllIAucFJlZJ3tDKyMSKS8mhwpzk3sPF1Xg4FjMyFnMpOSGkKZdL8uqraZrs7xVlJI7Rgp0t2LxKTv3yPbpALkN3s+S8sN/CSOkslRjZ0MGr5FC3THLGznictCyL/VwjUtjZzsCr5AQzdrYzdsbHoKhhJ1cnXEvO0XJxFLCcsbPctngothUZydUJ15LDCk3CexKb+wUMw0hyXd3zPEbq6gDHkhNCCprGZi+PB8uy2MkJZ5JVFJxJ0W7Fj/AtObO9PDYY1Mm2bV425EUEa9UiviUnTPbyOGEwMWZ2EhEPDI5x3Eue8G1VMP1j53IdLJTkVZW1MY57yVnr5fFT1nV2VhmKbcUkb1Jic7s+95ITQsq6nuRgzk7wZKcltGBzjBNBcgzmxbYiC8GczS4eG8yOcSJIThIfzFkY5pjt4rGRV1V2NsDMRBDJoZcnucxOfZgraFqSwzgU1VmbjQOCSE4IMU0zqyhsfssxAMMcrduwsNzF46Epl2OtqB4gjuSE7S86BigOcwn/5g3DYHlTllCS27aN08L4ZWO8i0cN3RyqHoSSnBDSWSoluQLnOI4speK8NAIu7E/y0kZB01hY2pgD0ST3PC+rKEm+krms63FeHcFsSTkeLMtivxghmuRkugiU5KQ9thkyJOqMd/Ho4GVNR0DJCSGdpRJT1/rFDCTtUafQcPt3TNRpt2J+xJTc8zys90YaY+EbTnKibhgG+4k6IKbkZDrOsFzzjJq8qkYXZ4ptRcyVeMlihJWcEGKaZpIn51CDjCKdwS+2MZPhqLgrsuRkOuBwkVNFQRTpDF9BLAqacjm+NvAKLjmJOGtlH4i6Ya2cw6jBfj05OngMG+JLDiUivobecCnreijZNX6TnaUSL8W2mYgvOZnelZXkUvDS4w8aHm5OFCeJkJxgnrk0z8Fw7tLUEOHXcJIcyQl6vljP0XDTNLmuNSZIcpJ4zz3Py6vqgnRFw8FwrvtMsiQn057j/LweadFwyNL5jeFA4iQn054nuYZUbCvO+8O6rus25XIFTUus4VBL53QePpMkSk6wB0/34NliFI6DxbaiGIaTxEpOZkxQE7s9c7bZJuSoib28R7xJSnIlB2DATux1LHDtfbGtGHRoiPCJ/UKCFEYYwwlKThIfuGDm0pTLOY4DqY0YOeoiMAxDllIcXXlSJyg5IYQ4jgMdPbGpe15VZSmVV1WRIlj9wNxt3mIkp6DkU3ieB5mqeAP53HieV9A0WFZszGQSWIyE+7QJ/MFR8r8CzndeVRMS0ms+byA813s/6sd1Xfi8YtcgUPJaIKTLUqqs66IO7WRG/77V58B8IXPXALh/k8ABPAAlvz22bTflcllFES+meZ5X1nVZSs1RQw5Gus5SSTwHbNvOKkpWUXjfylYnKPlcQOE9r6rC9AYIX3V+Itd186oKSw9iqG7bNnyiRFVeUPJ5gLgngOrwS2mLCF+BGFyrLsanWBwoeV3MVJ2vBD5o+RKnHjMl4asqaVlWYvUGUPIF4Hke3M8c7oLKeF93HKfYVoTV77ByENu2C5oG83nG85qak5VMvQGUfDFYlgV9vaBprAV213Whc8PSdxQjkeu6sKjO5mBnWVYwurF2dqiAki8e0Kkpl4PdzqZpUgwXQWPiHHqCwa4plzMMg+6SG7jN7NBDEZQ8BBzHCQSDXwiPJ5X1PM+yrM5SKasogdvxDzSe55mmCavuWUUpthUty4qnGfDNw55c+Nkm7tb2/fFvzvb8vvy+cfbiuB/NIVDyMHFd1zRNuCUDCN9ZKpmmGVbP8zzPtm3DMODuLkHPZmfDlm3bZV0H60B4wzBs2w7LecdxLMuqOYRpmnzGbb869OHRLXfKUkqWUnL6saN/cKoRHAYljwrXdYPuCM5nFQW0L+s6dP2AwAHXdWc+X9b1sq4X24pQHwarC5oWW7KwFGrGI1ibgMZD+wNmKjrzedM0y7reWSrB5XHBm5R13bIsPsWewQ37d7984/TgmE8mx/tLe9bI8k9+1Td2M/TjoOTxYds2aF/W9YKm5VUVHtB9g0fwfM2IwF0iWgOMX4ZhBN4GDxi/4NGUywXPByOCZVnsD2oLxf/e/mzwh+l/jZ49tlle/krPlcnQD4SSIwgLXOlr3tzY8scrEczLUXIEoY5fvaj/fE9H/3j4YZyg5AhCF3/kv08df+nRu2VZ2vDsW58MYyRHEPHwx785qxeeXSPL0qYjvZdD1xwlRxAW8K+db3tUSt2V7x0N+61RcgRhg8n+9gdXrG7uuxr2G6PkCMIGN794Z9t9e/VvMF1HEEHwx+2P3v+PTwbHfEIImRjqadn24rv2tfArbyg5glDBv97/9vZ0SpbWbtn184O7sk8fPjWAS2gIIhZ+deSrzyqVSqX/UjR6Ayg5gggOSo4ggoOSI4jgoOQIIjgoOYIIDkqOIIKDkiOI4KDkCCI4KDmCCA5KjiCCg5IjiOCg5AgiOCg5gggOSo4ggoOSI4jgoOQIIjgoOYIIDkqOIIKDkiOI4KDkCCI4KDmCCM6SJMcHPvDBxeP/AeYDbLKTU688AAAAAElFTkSuQmCC" alt></span></p>
<p><span>Write down the value of</span></p>
<p><span>(i) <em>q</em> ;</span></p>
<p><span>(ii) <em>p</em> and of <em>r</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>In the Venn diagram below, set <em>A</em> represents the people in the group with Australian passports and set <em>B</em> those with British passports.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find \(n(A \cup B')\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Police in a town are investigating the theft of mobile phones one evening from three cafés, “Alan’s Diner”, “Sarah’s Snackbar” and “Pete’s Eats”.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">They interviewed two suspects, Matthew and Anna, about that evening.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Matthew said:</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">“I visited Pete’s Eats and visited Alan’s Diner and I did not visit Sarah’s Snackbar.”</span></p>
<p style="text-align: left;"><span style="font-family: times new roman,times; font-size: medium;">Let \(p\) , \(q\) and \(r\) be the statements:</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">\(p\) : I visited Alan’s Diner</span><br><span style="font-family: times new roman,times; font-size: medium;">\(q\) : I visited Sarah’s Snackbar</span><br><span style="font-family: times new roman,times; font-size: medium;">\(r\) : I visited Pete’s Eats</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down Matthew’s statement in symbolic logic form.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>What Anna said was lost by the police, but in symbolic form it was</span></p>
<p><span>\[(q \vee r) \Rightarrow \neg p\]</span></p>
<p><span>Write down, in words, what Anna said.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following propositions.</p>
<p style="padding-left: 210px;"><em>p</em> : the baby cries<br><em>q</em> : the baby is happy<br><em>r</em> : the baby wants to play</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, in words, \(\left( {q \wedge r} \right) \Rightarrow \neg p\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the following truth table.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether \(\left( {q \wedge r} \right) \Rightarrow \neg p\) is a tautology, contradiction or neither.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the statements</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>p</em> : The numbers <em>x</em> and <em>y</em> are both even.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>q</em> : The sum of <em>x</em> and <em>y</em> is an even number.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down, in words, the statement <em>p </em>\(\Rightarrow\) <em>q</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down, in words, the inverse of the statement <em>p </em>\(\Rightarrow\) <em>q</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether the inverse of the statement<em> p</em> \( \Rightarrow \) <em>q</em> is always true. Justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the propositions <em>p</em> and <em>q</em>:</span></p>
<p><em><span>p: x is a number less than 10.</span></em></p>
<p><span><em><span><span>q: x2 is a number greater than 100.</span></span></em></span></p>
<p><span><span>Write in words the compound proposition \(\neg p \vee q\).</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using part (a), determine whether \(\neg p \vee q\) is true or false, for the case where \(x\) is a number less than 10 and \(x^2\) is a number greater than 100.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down a value of \(x\) for which \(\neg p \vee q\) is false.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1"> \(p:x\) is a multiple of \(12\)</p>
<p class="p1"> \(q:x\) is a multiple of \(6\)<span class="s1">.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down in words \(\neg p\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down in symbolic form the compound statement</p>
<p class="p2"><span class="s1">\(r:\) If \(x\) </span>is a multiple of \(12\)<span class="s1">, then \(x\) </span>is a multiple of \(6\)<span class="s1">.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Consider the compound statement</p>
<p class="p2"><span class="s1">\(s:\) If \(x\) </span>is a multiple of \(6\)<span class="s1">, then \(x\) </span>is a multiple of \(12\)<span class="s1">.</span></p>
<p class="p1">Identify whether \(s:\) is the inverse, the converse or the contrapositive of \(r\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Consider the compound statement</p>
<p class="p2"><span class="s1">\(s:\) If \(x\) </span>is a multiple of \(6\)<span class="s1">, then \(x\) </span>is a multiple of \(12\)<span class="s1">.</span></p>
<p class="p1">Determine the validity of \(s\). Justify your decision.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the statement<em> p</em>:</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">“If a quadrilateral is a square then the four sides of the quadrilateral are equal”.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the inverse of statement <em>p</em> in words.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the converse of statement <em>p</em> in words.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Determine whether the converse of statement <em>p</em> is always true. Give an example to justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The truth table below shows the truth-values for the proposition</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">\(p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q \Rightarrow \neg {\text{ }}p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } \neg q\)</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Explain the distinction between the compound propositions, \(p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q\) and \(p \vee q\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Fill in the four missing truth-values on the table.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether the proposition \(p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q \Rightarrow \neg p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } \neg q\) is a tautology, a contradiction or neither.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the propositions <em>p</em> and <em>q</em>.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>p</em>:<em> I take swimming lessons</em></span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>q</em>:<em> I can swim 50 metres</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the following compound proposition in symbolic form.</span></p>
<p><em><span>“I cannot swim 50 metres and I take swimming lessons.”</span></em></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the following compound proposition in words.</span></p>
<p><span>\(q \Rightarrow \neg q \)</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the universal set \(U = \{ x \in \mathbb{N}|3 < x < 13\} \), and the subsets \(A = \{ {\text{multiples of 3}}\} \) and \(B = \{ 4,{\text{ }}6,{\text{ }}12\} \).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of the following set.</span></p>
<p><span><em>A</em></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of the following set.</span></p>
<p><span>\(A \cap B'\)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down one element of \((A \cup B)'\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One of the statements in the table below is false. Indicate with an <strong>X</strong> which statement is false. Give a reason for your answer.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the two propositions <em>p</em> and <em>q</em>.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><em>p</em>: The sun is shining <em>q</em>: I will go swimming</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in words the compound proposition</span></p>
<p><span>\(p \Rightarrow q\) ;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in words the compound proposition</span></p>
<p><span>\(\neg p \vee q\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The truth table for these compound propositions is given below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Complete the column for \( \neg p\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The truth table for these compound propositions is given below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>State the relationship between the compound propositions \(p \Rightarrow q\) and \(\neg p \vee q\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Two propositions \(p\) and \(q\) are defined as follows</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em>\(p\): Eva is on a diet</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em>\(q\): Eva is losing weight.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the following statement <strong>in words</strong>.</span></p>
<p><span>\[q \Rightarrow p\]</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down, in words, the contrapositive statement of \(q \Rightarrow p\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Determine whether your statement in part (a) is logically equivalent to your statement in part (b). Justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Aleph has an unbiased cubical (six faced) die on which are written the numbers</p>
<p class="p1"><span class="s1">1 </span>, <span class="s1">2 </span>, <span class="s1">3 </span>, <span class="s1">4 </span>, <span class="s1">5 </span>and <span class="s1">6</span>.</p>
<p class="p1">Beth has an unbiased tetrahedral (four faced) die on which are written the numbers</p>
<p class="p1"><span class="s1">2 </span>, <span class="s1">3 </span>, <span class="s1">5 </span>and <span class="s1">7</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the Venn diagram with the numbers written on Aleph’s die (\(A\)) and Beth’s die (\(B\))<span class="s1">.</span></p>
<p class="p1"><span class="s1"><img src="images/Schermafbeelding_2015-12-20_om_06.18.17.png" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \(n(B \cap A')\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Aleph and Beth are each going to roll their die once only. Shin says the probability that each die will show the same number is \(\frac{1}{8}\).</p>
<p class="p2">Determine whether Shin is correct. Give a reason.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">Consider the following Venn diagrams. Each diagram is shaded differently.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-20_om_14.02.25.png" alt></p>
<p class="p1">In the following table there are six sets. Each of these sets corresponds to the shaded region of one of the Venn diagrams. In the correct space, write the number of the diagram that corresponds to that set.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-20_om_14.02.45.png" alt></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The probability that it snows today is 0.2. If it does snow today, the probability that it will snow tomorrow is 0.6. If it does not snow today, the probability that it will not snow tomorrow is 0.9.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the information given, complete the following tree diagram.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-20_om_08.12.00.png" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the probability that it will snow tomorrow.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">Consider two propositions <em>p</em></span> <span style="font-family: times new roman,times;">and</span> <span style="font-family: times new roman,times;"><em>q</em></span>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Decide whether the compound proposition</span><br><span>\[\left( {{\text{ }}p \Rightarrow \neg q} \right) \Leftrightarrow \left( {\neg p \Rightarrow q} \right)\]</span><br><span>is a tautology. State the reason for your decision.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Alan’s laundry basket contains two green, three red and seven black socks. He selects one sock from the laundry basket at random.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the probability that the sock is red.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Alan returns the sock to the laundry basket and selects two socks at random.</span></p>
<p><span>Find the probability that the first sock he selects is green and the second sock is black.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Alan returns the socks to the laundry basket and again selects two socks at random.</span></p>
<p><span>Find the probability that he selects two socks of the same colour.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(U\) is the set of <strong>positive </strong>integers less than or equal to \(10\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(A\), \(B\) and \(C\) are subsets of \(U\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em>\(A = \left\{ {{\text{even integers}}} \right\}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em>\(B = \left\{ {{\text{multiples of }}3} \right\}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em>\(C = \left\{ {6,{\text{ }}7,{\text{ }}8,{\text{ }}9} \right\}\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of \(A\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of \(B\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the Venn diagram with <strong>all </strong>the elements of \(U\).</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_17.36.22.png" alt></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A survey was carried out at an international airport. A number of travellers were interviewed and asked for their flight destinations. The results are shown in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One traveller is to be chosen at random from all those interviewed. </span></p>
<p><span>Find the probability that this traveller was going to Africa.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One female traveller is to be chosen at random from all those interviewed. </span></p>
<p><span>Find the probability that this female traveller was going to Asia.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One traveller is to be chosen at random from those <strong>not</strong> going to America.</span></p>
<p><span>Find the probability that the chosen traveller is female.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A fair six-sided die has the numbers 1, 2, 3, 4, 5, 6 written on its faces. A fair four-sided die has the numbers 1, 2, 3, and 4 written on its faces. The two dice are rolled.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The following diagram shows the possible outcomes.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAe8AAADsCAIAAADSCLmAAAAdqElEQVR4nO3d72sbV6LG8f4nI5g26ahWYrt+4VBwcpu2qH4hjHGybpNCWkXFCcklKUsClVCIKThQkLAcaqegyEQp7A00I/KDhdphMCwiURDVQijiwC6ESohihFcMO0aU4dwXRxqNZMlxdKw5iv18EMs2kWeOR853RmfGmrcogGiGYYgeAsAb7y3RA4D9rlwuT588KXoUAG881BwEW/xhUZZc6XRa9EAA3myoOYhULpdlySVLLhyeA3BCzUGkxR8W2bH59MmTODwH4IGagzDswJz9bzqdxuE5AA/UHHrJfJmaGZtI5M12f8kOzCmlsuSilOLwHIAHag69Uy2qlzySu23NrQNzWq85Ds8BeKDm0COmnr0ZuHo1oLSvuXVgTus1pzg8B+CAmkNv6Jmo/2a2uBpqV3P7gTm11RyH5wBdQ82hFzaykb9Gsxu0orWteTqdTqmq9Z9WzSmlwW+/tSoPADuHmsOuM/XszUAko1PaqeYt7DUHgO6g5rDb9Ews/KDI+v0m1DyXy62srAh8Q3A3mfzi9OlvLl8mhIgag3CFQiGlqoVCQdQADMNIp9PpdFrgpwZx/iii5rC7NrLz36eK1dp/9X3NT0xNvfv2O7LkGlAUTdOcH8CtpSX3gYPsF2IHFMX5oBuGsRBbYANYiC04vHZmIbZQfxXcN+bmnB9AuVweGRpmG2H48KDzOxXDME5MTVk/Cc+ePetiIag57KqKFlJc7Cey+XFqmWx2+iJRNU+n0wOKYg1y+PCg82OwIsIet+NxhwdwN5m0IuI+cPBuMunwAMrl8qH3Bqwt4D5w0PmY3pibs78KFy9ccHgAjx89sg/g4+PHu1gIag69tO2x+fT05y0Ph0d3Ox5v2es4PADaBzX/4vRp+wC+OH3a4QEQQuz7VFlyOf8G5fy58/YBTJ/8i8MDYJ9vwfmjiJpDL/X3TEs6nR5Q3JwHRJwWYgtiZ1q+OvOlPSLfXL7s8ACsT16zHs6fw7ibTNoHMHt91uEBpNNpNtfEHt5PPuliIag59FJ/15xSyqaMPzhyZGRoWNQpOHYW9KszX+ZyOefXTggRe1xMKdU0bdBz6IMjR2TJJeTshWEYXwcCA4oyMjT82fS0kBOhN+bmDr03MDI0/OHRY939KKLmIJ7Ya1rK5fJ+vpiEUlooFG7H47fjcYEX9hiGQQgRexeqQqEg8KIayv2jiJqDeLjeHIAfag7ioeYA/FBzEA81B+CHmoN4qDkAP9QcxEPNAfih5iAeag7ADzUH8VBzAH6oOYiHmgPwQ81BPNQcgB9qDuKh5gD8UHMQDzUH4Ieag3ioOQA/1BzEQ80B+KHmIB5qDsAPNQfxUHMAfqg5iIeaA/BDzUE81ByAH2oO4qHmAPxQcxAPNQfgh5qDeKg5AD/UHMRDzQH4oeYgHmoOwA81B/FQcwB+qDmIh5oD8EPNQTzUHIAfag7ioeYA/FBzEA81B+CHmoN4qDkAP9QcxEPNAfih5iAeag7ADzUH8VBzAH6oOfRItZRZDCguWXKPB1Wim9s8FTUH4IeaQy+Y+q8PkpmSSalZSsf8o56gVun8bNQcgB9qDj1g/ntt7ff60bhZ0cIeJaxVOh6eo+YA/FBz6LVNkjgzHsnonZ+BmgPwQ82hl3SiJcKB8Gppu2lz1BxgF6Dm0CNmRQt7JJcsuWRvOEW2mTYXXHPDMAgh5XJZ1AByudziD4u343FRYyCEsAEQQoQMgFJaLpfFvgr9oFAo8LwEqDn0VLWU/SnkdcvKpVSx2ulJAmuuadrw4cEPjhw59N7Ajbk55wfw+NEj94GDsuSSJdeg55DzOcvlctYABhRFSNA1TZMl14fHjsmSS9M05wdACPnqzJfTJ/9yY27OMAznB0ApvTE3N6AoHxw5MjI0XCgUulgCag49Z5LEhDQW0tY7PUFgzUeGhlnIZMk1oLidb5l9ALLkuh2POzyAr858aR/AN5cvOzyAcrlsH8CAoji8S2sZwNeBgJNrZ9LptLVPlSXXx8ePd7EQ1Bx6z8wv+z7aWvPp6c9bHg6Pq+WfsSy5Uqrq8BhaBrD4w6LDA/ji9Gn7AL4686XDAyCEDCiKfQwO71NTqtryKji5dmbxh0X+MaDm0HsVLTTYpzMtg55D1r+fd99+J5fLOTyA2euz1gDcBw46P4C7yaR1VOg+cPBuMunwAMrl8qH3BuzH5t3NM3RtZWVFeM0fP3pk36Xh2Bz6hVlUzym+0B3260NFLXwqkHjRn1coshlbNs0iZN7cMAwW9JGh4cePHjk/AErpraWlkaHhkaHhW0tLQgZwOx5nLRtQFOdfhXK5PHx40Nqfifox+Gx6ekBxs9Mn3e3UUXPoAf3Fsn+U/fPw+COp7PYXKAq+poVdTeHw8SC0YJdziHoVCoXCjbm58+fOO//WxI4QwnNhD2oO4uF6cwB+qDmIh5oD8EPNQTzUHIAfag7ioeYA/FBzEA81B+CHmoN4qDkAP9QcxEPNAfih5iAeag7ADzUH8VBzAH6oOYiHmgPwc7TmZin7MBEc9yXI9r/oLQ67JfFObrDQg3W/TM2Mtb/jmlnKPoiHvGeWyeaOF1ctZR8vBycnEvlXbOzWhVeL6iWPN5bVnXuRUHMAfm/JkkuWJqPZjaY/rmghpf6JYtven/c1mPlln1uWXHLf1lzPRP03s7rJPmZk+9vM776ONd8kiVOy5JKlUzuvuUkSE5JLltyvqvnWhaPmAG+kt3Sidrg1TLWoBv9Xfbmb/6ZZ0Pu05pskccrpgu8Ua+5r1JzWgv7Kmne58N2FmgPwe6txdNZ6OGZWtO+vdb5fTDf6uubrWnAMNRcCNQfgx2oejv68GFBcHn8y3wg6at4/UHMAeAVW89llUilp341L7vHwav2zqBs1b56Ete7Fzu70aOpk7X7k7PtB7T+1U4hsIfXb+0qjjTsV1Gq+qGXYX7nHgyqx7T908kuUnYRUzkZXiU4ppRWi3Yv6faHVfz6fP+tRZpbzW3tbIVoi5HU3fyGlOtF+jgQmE6SSTwV9stSyu7LY7i7PHrX9TdvFtkw0r2vBMdvZhZ2MllKdjWc0EFGfrz3NVUz7ZrS+wCxlkrVhL96PTDcFVydPImc9kkuWRgORXxrb0Cxl7wTHJZeszNz++fttat5x4WyjDdpOlnRa1+5BzQH4WTXfpLSST8x4GvFtPjavaCGlkYbGfXvr50vrNyUw9WxsXBoNRO5ppEJptaR9N26VgtXcG0yyZxI15HV7ZtSiSSk19eyPofl0if3/fDKgjIW0P+qdHQ3Mp0uVTNQ73XrCllaL6qX3a5muEDU8XvsW6p31XozeeVoyW7+FVmZ+2ee2HZt3Wiyt199q6yZJnJKVsFb5cwejZc+fOVc7IVEtPri3VjEbm7E+ALO0es07eU0rmpSapbWY/yNbcDOx4I/PS1VKadMJW7OohSdr+2OzuDY/80mHmndeeMvOqfO6dhVqDsDPXnOWA58s+a5pRXOHNadbOviqZ9pmWuxZrHfE9vAEtUrtOZ3v+F7RQor9bzeykcl6jNa14Fhjda29btbmu+i02E41t/5qu/vTUzO/7BsLRNRsqbrlz60BbGQjk7ah2idDtryTqMX3Tz0bG7ddgNR5pmWbhbf9draua5cPz1FzAH7NNafWPcAmo9ly72vecozfdup2+z62hLXl+V3XfPvF7rzmLTVkf14tqpc8bPbm5zXbJIltAK1vI+zBXdeCH7VrdPM3u03Nt1t4y7fTaV27DDUH4Lel5rW34W5ZuXg7PutszdseSO6k5va/3cWad1osZ81p/Vd7fLLkalwb+ho1H2t3JrlHNW+7rl2GmgPwa1NzWrvnur0+vZxpqV0ZyWZa6jd6p5TSjZz2z53NtLhtv3RjVrSwZ3dmWjotlm+mxb7OUjrWmPW2DaB1qGzj2Gda3OPBn+pzNab+6z+ylf/ahkGtp7Wp+XYLb/vtbF0XZloA+s5blG5kI2e31IedzLRViSVgRi2a9V/Qt65y2XnNWTiazoLWzsXV12ifomW/ofrKPrKTt76Qmtcpmyn6tH6OkaPm2y2WfVOj59SXpv0oWzq1TP67g5qvr6lPa2sxX6ZmxmrbqmkAbDZmNDCfLpmmnn8Qnfm0cSGNnomyK21qj9peh+2DPf7F56Uq1X9LRS42XqOmAWy78Kaa007r2l2oOQC/tyZaL8uzVItq2Ha9ObvOxCVLvpCar5DEhDe4/CBbzCfsS8jb/tMTXP3dNs9QP+osZdVIoHYZTOxJ02ehWBc1WlcEWpcDuj/xfjrVcQK3QlZjbJmyN7isEZ3aPkiAnbj7fbXxWQWt32nLfIiVv3aLra8xn5jx1D7O5Q+SODMejD/M/ju/o9GWc9rfn6jxkNfdeC9i/ygF6/rI2tpHA4lMtraK2vsW6/rC5qsGG5d4evzJ37Jx9hqV2oyj08Lt56JrR+sd1rWbUHMAfvgMRRAPNQfgh5qDeKg5AD/UHMRDzQH4oeYgHmoOwA81B/FQcwB+qDmIh5oD8EPNQTzUHIAfag7ioeYA/FBzEA81B+CHmoN4qDkAP9QceqZx0yL753a1gZoD8EPNoTfMlw/nf2Sfw8M+KnLLbcQbUHMAfqg59IT5r/RasXEw3vxRmq1QcwB+qDk4ovXOfE1QcwB+qDk4oqKFBut3WdpCbM0JIVevXLl65Uoul3N+7YZhfHP5siy5Pj5+/NmzZ84PgFJaKBROTE3JkuvE1FShUBAyhnQ6nVJVUWunlN6/f//8ufM35ubK5bKQARQKhRtzc+fPndc0rbsloObgALOizU50vs2FwJrncjn3gYPsI93dBw4639OvAwHrZiADiuJ8zgzDGD48aI1h+PCgYRgOD+DE1BR7FQYUpeuW8ViILVg/Bs5vAUppuVwe9Byyfg5vLS11sRDUHHpPz0T9NzudAqVCa371yhXbnZVcX5w+7fAA7GuXJVdKVR0eACHEChlLCSHEyQGsrKwMKIp9d+Lk2pmWV2FlZcXhAdxNJlvG0MVCUHPotY3s/HfL+Tb375ue/rzl4fzgzp8731c1d74jhJABpXGzwEHPIYffH9yOx/lDxkn4PnVXNgJqDj1VLT74Mdku5XYCj801TXv37Xesw9K7yaTDA7C/xx8ZGnb+PT6l9LPpaSsin01PO7z2XC5n3518fPy4wwOgzfNdsuRyfuq85R3S7PXZLhaCmkPvVEvaj7HaXbwppZX8nZ/WKm3mW8SeBb33f/83OTHx4dFjzqec0TRt9vrsraUlUeffDMO4f//+1StX7t+/L2R3shBbYDuzD48eE3Ii1DCM2euzI0PDJ6amhJwMp5Q+e/ZscmJiZGj4xtxcd68Cag49UiFqeLz5zeOW+2vX4ApFMAxD4AUtewNqDr1QLaqXPC0pl9wTiXzbM6GoOQA/1BzEQ80B+KHmIB5qDsAPNQfxUHMAfqg5iIeaA/BDzUE81ByAH2oO4qHmAPxQcxAPNQfgh5qDeKg5AD/UHMRDzQH4oeYgHmoOwA81B/FQcwB+qDmIh5oD8EPNQTzUHIAfag7ioeYA/FBzEA81B+CHmoN4qDkAP9QcxEPNAfih5iAeag7ADzUH8VBzAH6oOYiHmgPwQ81BPNQcgB9qDuKh5gD8UHMQDzUH4Ieag3ioOQA/1BzEQ80B+KHmIB5qDsAPNQfxUHMAfqg5iIeaA/BDzUE81ByAH2oO4qHmAPxQcxAPNQfgh5qDeKg5AD/UHMRDzQH4oebQMzrR1L9F/b6Qtr79E1FzAH6oOfSGmV+ePBU4MypLY6g5gANQc+ghkyQm3oSaE0IMwxA4gHQ6vbKyUi6XRQ2gUCiI3QKGYRQKBYED2ANQc+ih/q95oVAYGRoeGRqWJdetpSXnB2AYxompKfeBg7LkkiXXs2fPHB5AoVD48OgxtgUWYgsOr51ZiC3IkmtkaPjDo8eENL1QKHxz+bIsuS5euCBkAIZh3FpaGhkanpyY0DStu4Wg5tBD/V/zD48eYxmVJZf7wEFCiMMDePzokTUAWXJ9fPy4wwP4+Phxa+0DijuXyzk8gFwuN6C4BW4B2vxjMHx40Pm3KTfm5uw/h929Cqg59ND2NZ+e/rzl4fDwyuWyvaSy5EqpqsNjWPxhsWUMDg+gZe2343GHB3A7Hhe7BQgh7K2J9XB+p94ygNnrs10sBDWHHur/Y3P7P6F3334nnU47PABN0959+x1rDF+d+dLhAQwfHrQdmysrKysOD+Dxo0cDimI/NHZ4AGy2TexbtJaadzflhZpDD/V/zTVNYyl59+13TkxNCRnDjbm5Q+8NiJo1traA+8DBE1NTzk8y2M8cDChK17PGPL4OBKySCvkxuJtM2nfq3f0YoObQQ/1fc0ppoVBIqarz88V25XLZ+eNBC9sCzr8vsUun0ylVFXVZi2EYd5PJ8+fO31paEnVtj6ZpV69cmb0+2/VGQM2hh96ImgPsDag59BBqDuAY1Bx6ZF0LjjVO7PgSxOz4VNQcgB9qDuKh5gD8UHMQDzUH4Ieag3ioOQA/1BzEQ80B+KHmIB5qDsAPNQfxUHMAfqg5iIeaA/BDzUE81ByAH2oO4qHmAPxQcxAPNQfgh5qDeKg5AD/UHMRDzQH4oeYgHmoOwA81B/FQcwB+qDmIh5oD8EPNQTzUHIAfag7ioeYA/FBzEA81B+CHmoN4qDkAP9QcxEPNAfih5iAeag7ADzUH8VBzAH6oOYiHmgPwQ81BPNQcgB9qDuKh5gD8UHMQDzUH4Ieag3ioOQA/1BzEQ80B+KHmIB5qDsAPNQfxUHMAfqg5iIeaA/BDzUE81ByAH2oO4qHmAK80ffJk8NtvCSGdnoCag3io+fT056KHAP3OMIyUqv7P0aOdmo6ag3jCay48psIH0A9jED6AN8I2TUfNQTzUXPgA+mEMGMDOx9C26ag5iCdLLrGP6enP9/kA+mEMGADPGAzDQM0BxB+UCR9AP4wBA3itMViH54s/LJbLZYpjcwDaB/+MhQ+gH8aAAexwDFs7zqDmAOL/GQsfQD+MAQN45Rg6dZxBzQEA3gArKyudOs6g5gAAb4CVlZVOHWdQcwCAvQA1BwDYC1BzAOgb5svUzNhEIm+KHsibCDWH/U0nmvq3qN8X0tZFrN7UyS9R/6gsuWTJF7qTKe3rjFWL6iWP5BZQ84oWUqzfxDm1TDYdXv+uQM1hHzPzy5OnAmdGZWlMSM3N4t9j878Q3aS0WsosBhT3eCSjOzyGUjrGdifecIpUnF1500D07M3A1asBxfmas71Ivea+BBG1TzVL2Qd/i/q7/IFEzWG/M0liQkzNN/+19rTYCMcmSZySlbBWcbAl+j9Td56WTErN0vP5sx6H1940kkzUfzNbXA05X3M9E/XNCvvG69hu1eOP3NdId3t01Bz2O3E1bx1IRQs729Pm3UlFCymitsNGNvLXaHaDVjTHa25WtLBHco8H46luM7oL9EzUOxaYT/NMtaHmsN/1Vc3fn1GLgo4RTZKY8MayuvOrN/XszQCbYnK+5mZ+2eeuz5i7x4MqEbAFNrKRSQ/3S4+aw37XNzVf14Jno9kNEauuEC0R8t/QSlUBK9czsfCDWsgEHJtTStmEdTzkdcuSiFMXJDEh+UKJn9j5cI8/9qSrExioOex3/VFz2/GpwxqXc/hCat7xAWxk579PFet7EVE1Z8yiFvY5feqCnS/xBpPZkkkp1V8s+0flrt4koeaw3/VFzfVMLPhTXsB7/BqzlEkGfbI0ek596eggmi4NtD8EXSYo4OTBuhYc8wQ162jcJImJri7TRM1hvxNfc/Plw/l7AlNeH0Z+2ee2Z0UAscfmlG2EM47uSLZu9m5fCNQc9jvBNTeL2vyPjQlr/UUykRbU002SOLXfa17RroUd3gLrWnCs6SJ3M7/sG8KxOcBrE1lzPZ8K+ppnGAS2bF0L+pyeaWnheM3NUvbhAzZjTc1SOhaMOH4qmF2Zeqn55EE3E02oOexn61pwTBb1S4Dmy9TMqMj5YvNlamZsPPhTtlSltFrSvpvwJ8VP+DjLLK1e87plySUrZ6M/r4m4PLH2k+BhG98sPZ+fmejqfDhqDrBvVfKJmdpvtCtno2p2f39KjFA6eRI56+H7uB7UHABgL0DNAQD2AtQcAGAvQM0BAPYC1BwAYC9AzQEA9gLUHABgL0DNAQD2AtQcAGAvQM0BAPYC1BzgDVItZR8vBydFfsrgazKL6jllcjfvqcQ+XqbtJ5nUbiH0Wh9pu/NN2vLMalG95BFz7732UHOA7pkkMcE+56T1XzW7d3Dts7R262Nm66sT+pmxr8nBmm+SxKnX/eSynW/SLc9EzQH2mgpRw+OSq81des2XqQvBxied7oaub0yzP7Cgv97nUO58k/b5xkfNAbjV7vu+9QbB61r4+929yWSfB0U01BwAeJj55QuR+/EZjzQaSLywBR01dxhqDgA8zPzyhST5s6iFfbLku6ZZMy5WzVumdOt3yajdHt7Uydr9yNn3g9p/SumYf1SW3OPh1ZJZLWV/Cnndsm0nUQtKfPX5neA4+zhsNW/bf1TIaiyguGTJ5fHHnpAKpZTqRPs5EhgMP8n/I+av3xWhhU60BFug7Qutr51MkErtNkntv5ytms04+SOpTPr5r+XaH2r3on5fSFtvujeIL0E26vd3rm2Edmr3ZhoNRNTna09zzduqcVvk2i2qXR7/4v3IdFPNG58bPhqI/NK4GYVZyrINqMzc/vn77Rrd6Zn1rdoYfKd1OQU1B+DGam5Sqr9Y9o/KysxynqXGfmzOzotaodkkiVO1kNXvW+/xR1LZkklNPRsbl0YDkXsaqbC7Ao3Xv5DVvH7DIBbQ0frt3zay87Ox2q0OKvnEjEcJa5U/6nuOs7FMsZKNjW89cWe+TM18WtthsIDWvoV6f70Xo3eelszt7vRmksRU/cyBWfwlubZuOxVs3aiP3R+D7fAq+cTFiaDauXqbJDFT/9aqxQf31uzbql5zs7R6zTvJ9qBmaS3m/6hRcz0TC/74nN0ZTn+x7B+tfZVZ1MKT4+HVkkmpWVybn/mkU807PrNlf9x5XQ5CzQG4WTW37kzm/U4rVXdac7rlNu3N0bTfuXTLm33bPYLrpbM9xhoHxR0Pgdl9Ke3HmJmo1xpM8z2IO95OfpMkTtX3Rs1Lb73t6kY2MilLvlBkNtQ0K9Vuq/rGAhE123KjzqYxbGQjk7bx2Gdami4rqj2UsFb5U8/Gxm3fb+f5E3PbZ9pfwU7rcvTwHDUH4GarOaWmnk8GFHbN4h+9r7m1nD8rWtjT/tam29d8yz3jm56/w5qzKxHZJAN7S1H/86030TaLWtgn2+9r3FpD9vxqUb3k2XrHTvsYWt8r2Gu+rgU/atfo1u+3c823f6b9Fey0Lkeh5gDcmmpO63MjLs/MzdtBZ2ve/gTgDmre9Lfd1JxSapayD2uT79bkT7ua65mo/6+hphn8tjWn9V/Y8cmSq1H/16j5WLs7d/eo5m3X5SjUHIBba82p7bgy3PuZlo9qV0aymRZvMGlNd+gvtGx5RzMtkv0XfNa14NhrzrTYl1d6Pn/WmrpprblZ1K7fSBWrZmn1mneoNiX9yg1cSscas962MbSOh01n22darHMMlFJT//Uf2cp/m7Z8/Wntar657TO3zrRsXRdmWgDeLHom6pvd0sqNbGRSbp11ZQettkNOlp4d15z9VdNZ0NocfX2N9qnb2gnP7WteP3nrDadIpTZTNGhNg+yw5mZl7fFabfnVonrJmvNpGrxZ1MJnrLKzDRKYT3cI+vqa+rS2IvNlamastkGaxsD2mmwhpp5/EJ35tLFV9UzU67ZtkNovBLBJIY9/8XmpSvXfUpGL4x1+HXTbZza3vsO6nISaA/CwLj1slwPzZerCDVtD2RUdLtkbTpE/SOLMeDD+MFv60/p4AMkl+xL5fOM/PcHV37d8QoBZyqY6XQlnXU5nXWhY+80mlyyNjXvPdrwQu3F1nXs8mKhNfDe+1iUrYe331cZZ1tZZBbPyq/ZwVV0O+uTGIap9/sQ9kfg1z7ZV85U87ZbGlHPa35+o8ZDXLUu+0J1M/aKalq+yLsocDSQy2fpWre196hcvNm8rUye/RP2j7ILL37LxCW9w+cGWE7jbPdN2taV1uVH7dTkHNQcA2AtQcwCAvQA1BwDYC/4fz3ELKOIEQEUAAAAASUVORK5CYII=" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that the two dice show the same number.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that the difference between the two numbers shown on the dice is 1.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that the number shown on the four-sided die is greater than the number shown on the six-sided die, given that the difference between the two numbers is 1.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the following truth table.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the propositions</span></p>
<p><span><span> </span><em><span>p</span></em><span>:</span><em><span> Cristina understands logic</span></em></span></p>
<p><span> </span><em><span>q</span></em><span>:</span><em><span> Cristina will do well on the logic test.</span></em></p>
<p><span>Write down the following compound proposition in symbolic form.</span></p>
<p><em><span>“If Cristina understands logic then she will do well on the logic test”</span></em></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down in words the contrapositive of the proposition given in part (b).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">In a particular school, students must choose at least one of three optional subjects: art, psychology or history.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the following propositions</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><em>a: I choose art,</em></span><br><span style="font-family: times new roman,times; font-size: medium;"><em>p: I choose psychology,</em></span><br><span style="font-family: times new roman,times; font-size: medium;"><em>h: I choose history.</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write, in words, the compound proposition</span><br><span>\[\neg h \Rightarrow (p \vee a)\].</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table for \(\neg a \Rightarrow p\) .</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether \(\neg a \Rightarrow p\) is a tautology, a contradiction or neither. Justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Two propositions are defined as follows:</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> \(p:\) <em>Quadrilateral ABCD has two diagonals that are equal in length.</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> \(q:\) <em>Quadrilateral ABCD is a rectangle.</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Express the following in symbolic form.</span></p>
<p><span><em>“A rectangle always has two diagonals that are equal in length.”</em></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down in symbolic form the converse of the statement in (a).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Determine, <strong>without </strong>using a truth table, whether the statements in (a) and (b) are logically equivalent.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the name of the statement that is logically equivalent to the converse.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following propositions.</p>
<p>\[\begin{array}{*{20}{l}} {p{\text{: The car is under warranty}}} \\ {q{\text{: The car is less than 2 years old}}} \\ {r{\text{ : The car has been driven more than 20}}\,{\text{000 km}}} \end{array}\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down in words \((q \vee \neg r) \Rightarrow p\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the truth table.</p>
<p><img src="images/Schermafbeelding_2018-02-13_om_06.43.42.png" alt="N17/5/MATSD/SP1/ENG/TZ0/04.b"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether the statement \(\neg p \Rightarrow \neg (q \vee \neg r)\) is the inverse, the converse or the contrapositive of the statement in part (a).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The following Venn diagram shows the relationship between the sets of numbers</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\[\mathbb{N},{\text{ }}\mathbb{Z}{\text{, }}\mathbb{Q}{\text{ and }}\mathbb{R}{\text{.}}\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The number –3 belongs to the set of \(\mathbb{Z}{\text{, }}\mathbb{Q}\) and \(\mathbb{R}\), but not \(\mathbb{N}\), and is placed in the appropriate position on the Venn diagram as an example.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-02_om_14.14.57.png" alt><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the following numbers in the appropriate place in the Venn diagram.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>4</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(\frac{1}{3}\)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(\pi \)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(0.38\)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(\sqrt 5 \)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(-0.25\)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the following logic propositions:</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(p:{\text{ Sean is at school}}\)</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(q:{\text{ Sean is playing a game on his computer}}{\text{.}}\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in words, \(p \underline { \vee } q\)</span><span>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in words, the converse of \(p \Rightarrow \neg q\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the following truth table for \(p \Rightarrow \neg q\).</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the following logic propositions:</span></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">p </span></em><span style="font-size: medium; font-family: times new roman,times;">:</span><em><span style="font-size: medium; font-family: times new roman,times;"> Yuiko is studying French.</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">q </span></em><span style="font-size: medium; font-family: times new roman,times;">:</span><em><span style="font-size: medium; font-family: times new roman,times;"> Yuiko is studying Chinese.</span></em></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the following compound propositions in symbolic form.</span></p>
<p><span>(i) Yuiko is studying French but not Chinese.</span></p>
<p><span>(ii) Yuiko is studying French or Chinese, but not both.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down in words the <strong>inverse</strong> of the following compound proposition.</span></p>
<p><em><span>If Yuiko is studying Chinese, then she is not studying French.</span></em></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A class consists of students studying Spanish or French or both. Fifteen students study Spanish and twelve study French.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The probability that a student studies French given that she studies Spanish is \(\frac{{7}}{{15}}\)</span><span style="font-size: medium; font-family: times new roman,times;">.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn diagram in the space below to illustrate this information.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that a student studies Spanish given that she studies one language only.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the following logic propositions. </p>
<p class="p1" style="padding-left: 60px;"> \(p\): Sandi gets up before eight o’clock</p>
<p class="p1" style="padding-left: 60px;"> \(q\): Sandi goes for a run</p>
<p class="p1" style="padding-left: 60px;"> \(r\): Sandi goes for a swim</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down in words the compound proposition</p>
<p class="p1"><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the following truth table.</p>
<p class="p1"><img src="images/Schermafbeelding_2017-03-06_om_13.42.11.png" alt="N16/5/MATSD/SP1/ENG/TZ0/05.b"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">On a morning when Sandi does </span><strong>not </strong>get up before eight o’clock, use your truth table to determine whether \(p \Rightarrow (q{\text{ }}\underline \vee {\text{ }}r)\) is a tautology, contradiction or neither.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Peter either walks or cycles to work. The probability that he walks is <span class="s1">0.25</span>. If Peter walks to work, the probability that he is late is <span class="s1">0.1</span>. If he cycles to work, the probability that he is late is <span class="s1">0.05</span>. The tree diagram for this information is shown.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-20_om_07.11.52.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">On a day chosen at random, Peter walked to work.</p>
<p class="p1">Write down the probability that he was on time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">For a different day, also chosen at random,</p>
<p class="p1">find the probability that Peter cycled to work and was late.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">For a different day, also chosen at random,</p>
<p class="p1">find the probability that, given Peter was late, he cycled to work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A bag contains 7 red discs and 4 blue discs. Ju Shen chooses a disc at random from the bag and removes it. Ramón then chooses a disc from those left in the bag.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the probability that</span></p>
<p><span>(i) Ju Shen chooses a red disc from the bag;</span></p>
<p><span>(ii) Ramón chooses a blue disc from the bag, given that Ju Shen has chosen a red disc;</span></p>
<p><span>(iii) Ju Shen chooses a red disc and Ramón chooses a blue disc from the bag.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Ju Shen and Ramón choose different coloured discs from the bag.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The Home Shine factory produces light bulbs, 7% of which are found to be defective.</p>
</div>
<div class="specification">
<p>Francesco buys two light bulbs produced by Home Shine.</p>
</div>
<div class="specification">
<p>The Bright Light factory also produces light bulbs. The probability that a light bulb produced by Bright Light is not defective is \(a\).</p>
<p>Deborah buys three light bulbs produced by Bright Light.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that a light bulb produced by Home Shine is not defective.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that both light bulbs are not defective.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least one of Francesco’s light bulbs is defective.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in terms of \(a\), for the probability that at least one of Deborah’s three light bulbs is defective.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">In a research project on the relation between the gender of 150 science students at college and their degree subject, the following set of data is collected.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that a student chosen at random </span><span>is male.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that a student chosen at random </span><span>is either male or studies Chemistry.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that a student chosen at random </span><span>studies Physics, given that the student is male.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table shown below.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether the compound proposition \((p \vee (p \wedge q)) \Rightarrow p\) is a contradiction, a tautology or neither.</span></p>
<p> </p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the following propositions.</span></p>
<p><span> </span><em><span>p: Feng finishes his homework</span></em></p>
<p><span> </span><em><span>q: Feng goes to the football match</span></em></p>
<p><span>Write in symbolic form the following proposition.</span></p>
<p><em><span>If Feng does not go to the football match then Feng finishes his homework.</span></em></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The Venn diagram shows the numbers of pupils in a school according to whether they study the sciences Physics (\(P\)), Chemistry (\(C\)), Biology (\(B\)).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of pupils that study Chemistry only.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Write down the number of pupils that study</span> <span><strong>exactly</strong> two sciences.</span></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of pupils that do not study Physics.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(n[(P \cup B) \cap C]\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the following logic statements.</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"><em>p: Carlos is playing the guitar</em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"><em>q: Carlos is studying for his IB exams</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in words the compound statement \(\neg p \wedge q\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the following statement in symbolic form.</span></p>
<p><span><em>“Either Carlos is playing the guitar or he is studying for his IB exams but not both.”</em></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the <strong>converse</strong> of the following statement in <strong>symbolic form</strong>.</span></p>
<p><em><span>“If Carlos is playing the guitar then he is not studying for his IB exams.”</span></em></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In the Canadian city of Ottawa:</p>
<p>\[\begin{array}{*{20}{l}} {{\text{97% of the population speak English,}}} \\ {{\text{38% of the population speak French,}}} \\ {{\text{36% of the population speak both English and French.}}} \end{array}\]</p>
</div>
<div class="specification">
<p>The total population of Ottawa is \(985\,000\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the percentage of the population of Ottawa that speak English but not French.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of people in Ottawa that speak both English and French.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down your answer to part (b) in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\) and <em>k </em>\( \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Rosewood College has 120 students. The students can join the sports club (\(S\)) and the music club (\(M\)).</p>
<p>For a student chosen at random from these 120, the probability that they joined both clubs is \(\frac{1}{4}\) and the probability that they joined the music club is\(\frac{1}{3}\).</p>
<p>There are 20 students that did not join either club.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the Venn diagram for these students.</p>
<p><img src="images/Schermafbeelding_2018-02-13_om_08.15.35.png" alt="N17/5/MATSD/SP1/ENG/TZ0/07.a"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>One of the students who joined the sports club is chosen at random. Find the probability that this student joined both clubs.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine whether the events \(S\) and \(M\) are independent.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the propositions</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em>\(p\): <em>I have a bowl of soup.</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em> \(q\): <em>I have an ice cream.</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down, in words, the compound proposition \(\neg p \Rightarrow q\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_17.49.25.png" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down, in symbolic form, the converse of \(\neg p \Rightarrow q\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following propositions.</p>
<p>\[\begin{array}{*{20}{l}} {p{\text{: I completed the task}}} \\ {q{\text{: I was paid}}} \end{array}\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down in words \(\neg q\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down in symbolic form the compound statement:</p>
<p>If I was paid then I completed the task.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the following truth table.</p>
<p><img src="images/Schermafbeelding_2017-08-15_om_13.11.00.png" alt="M17/5/MATSD/SP1/ENG/TZ1/03.c.i"></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether the statements \(p \vee \neg q\) and \(q \Rightarrow p\) are logically equivalent. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \({\text{P}}(A) = 0.5\), \({\text{P}}(B) = 0.6\) and \({\text{P}}(A \cup B) = 0.8\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \({\text{P}}(A \cap B)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \({\text{P}}(A|B)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Decide whether <em>A</em> and <em>B</em> are independent events. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two friends, Sensen and Cruz, are conducting an investigation on probability.</p>
<p>Sensen has a fair six-sided die with faces numbered \(1,\,\,2,\,\,2,\,\,4,\,\,4\) and \(4\). Cruz has a fair disc with one red side and one blue side.</p>
<p>The die and the disc are thrown at the same time.</p>
<p>Find the probability that the number shown on the die is \(1\) <strong>and</strong> the colour shown on the disc is blue;</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the number shown on the die is \(1\) <strong>or</strong> the colour shown on the disc is blue;</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the number shown on the die is even given that the colour shown on the disc is red.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the propositions \(r\), \(p\) and \(q\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the following truth table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-20_om_13.45.17.png" alt></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Determine whether the compound proposition \(\neg \left( {(r \wedge p) \vee \neg q)} \right) \Leftrightarrow \neg (r \wedge p) \wedge q\) <span class="s1">is a tautology, a contradiction or neither.</span></p>
<p class="p2">Give a reason.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the following statements</p>
<p>\(z\,:\,x\) is an integer<br>\(q\,:\,x\) is a rational number<br>\(r\,:\,x\) is a real number.</p>
<p>i) Write down, in words, \(\neg q\).</p>
<p>ii) Write down a value for \(x\) such that the statement \(\neg q\) is true.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write the following argument in symbolic form:<br>“If \(x\) is a real number and \(x\) is not a rational number, then \(x\) is not an integer”.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Phoebe states that the argument in part (b) can be shown to be valid, without the need of a truth table.</p>
<p>Justify Phoebe’s statement.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Ramzi travels to work each day, either by bus or by train. The probability that he travels by bus is \(\frac{3}{5}\). If he travels by bus, the probability that he buys a magazine is \(\frac{2}{3}\). If he travels by train, the probability that he buys a magazine is \(\frac{3}{4}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-03_om_06.15.58.png" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Ramzi buys a magazine when he travels to work.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;"><em>B</em> and <em>C</em> are subsets of a universal set <em>U</em> such that</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">\(U = \left\{ {x:x \in \mathbb{Z},0 \leqslant x < 10} \right\},{\text{ }}B = \left\{ {{\text{prime numbers}} < 10} \right\},{\text{ }}C = \left\{ {x:x \in \mathbb{Z},1 < x \leqslant 6} \right\}.\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the members of sets</span></p>
<p><span>(i) \(B\)</span></p>
<p><span>(ii) \(C \cap B\)</span></p>
<p><span>(iii) \(B \cup C′\)</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the propositions:</span></p>
<p><span><em>p</em> : <em>x</em> is a prime number less than 10.</span></p>
<p><span><em>q</em> : <em>x</em> is a positive integer between 1 and 7.</span></p>
<p><span>Write down, in words, the contrapositive of the statement, “If <em>x</em> is a prime number less than 10, then <em>x</em> is a positive integer between 1 and 7.”</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Tuti has the following polygons to classify: rectangle (R), rhombus (H), isosceles triangle (I), regular pentagon (P), and scalene triangle (T).</p>
<p class="p1">In the Venn diagram below, set \(A\) consists of the polygons that have at least one pair of parallel sides, and set \(B\) consists of the polygons that have at least one pair of equal sides.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-03_om_08.19.15.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the Venn diagram by placing the letter corresponding to each polygon in the appropriate region. For example, R has already been placed, and represents the rectangle.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State which polygons from Tuti’s list are elements of</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(A \cap B\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\((A \cup B)'\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the following statements about the quadrilateral ABCD</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">\(q:\) ABCD has four equal sides \(s:\) ABCD is a square</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Express in words the statement, \(s \Rightarrow q\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down in words, the inverse of the statement, \(s \Rightarrow q\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Determine the validity of the argument in (b). Give a reason for your decision.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A survey was carried out in a group of 200 people. They were asked whether they smoke or not. The collected information was organized in the following table.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">One person from this group is chosen at random.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the probability that this person is a smoker.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the probability that this person is male given that they are a smoker.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that this person is a smoker or is male.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">On a work day, the probability that Mr Van Winkel wakes up early is \(\frac{4}{5}\).</p>
<p class="p1">If he wakes up early, the probability that he is on time for work is \(p\).</p>
<p class="p1">If he wakes up late, the probability that he is on time for work is \(\frac{1}{4}\).</p>
</div>
<div class="specification">
<p class="p1">The probability that Mr Van Winkel arrives on time for work is \(\frac{3}{5}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the tree diagram below.</p>
<p class="p1"><img src="images/Schermafbeelding_2017-03-07_om_06.20.32.png" alt="N16/5/MATSD/SP1/ENG/TZ0/12.a"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(p\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following Venn diagram shows the sets \(A\), \(B\), \(C\) and \(U\).</p>
<p class="p1">\(x\) is an element of \(U\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-06_om_09.16.47.png" alt="N16/5/MATSD/SP1/ENG/TZ0/03"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">In the table indicate whether the given statements are True or False.</p>
<p class="p1"><img src="images/Schermafbeelding_2017-03-06_om_12.54.23.png" alt="N16/5/MATSD/SP1/ENG/TZ0/03.a"></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">On the Venn diagram, shade the region \(A \cap (B \cup C)'\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Sara regularly flies from Geneva to London. She takes either a direct flight or a non-directflight that goes via Amsterdam.</p>
<p>If she takes a direct flight, the probability that her baggage does not arrive in London is 0.01.<br>If she takes a non-direct flight the probability that her baggage arrives in London is 0.95.</p>
<p>The probability that she takes a non-direct flight is 0.2.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_11.08.43.png" alt="M17/5/MATSD/SP1/ENG/TZ1/07"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the tree diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Sara’s baggage arrives in London.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The IB grades attained by a group of students are listed as follows.</p>
<p class="p1">\[{\text{6}}\;\;\;{\text{4}}\;\;\;{\text{5}}\;\;\;{\text{3}}\;\;\;{\text{7}}\;\;\;{\text{3}}\;\;\;{\text{5}}\;\;\;{\text{4}}\;\;\;{\text{2}}\;\;\;{\text{5}}\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the median grade.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the interquartile range.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the probability that a student chosen at random from the group scored at least a grade \(4\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A <strong>weighted</strong> die has 2 red faces, 3 green faces and 1 black face. When the die is thrown,</span> <span style="font-size: medium; font-family: times new roman,times;">the black face is three times as likely to appear on top as one of the other five faces. </span><span style="font-size: medium; font-family: times new roman,times;">The other five faces have equal probability of appearing on top.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The following table gives the probabilities.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of</span></p>
<p><span>(i) <em>m</em>;</span></p>
<p><span>(ii) <em>n</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The die is thrown once.</span></p>
<p><span>Given that the face on top is not red, find the probability that it is black.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The die is now thrown twice.</span></p>
<p><span>Calculate the probability that black appears on top both times.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Complete the truth table below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>(ii) State whether the compound propositions \(\neg (p \wedge q)\) and \(\neg p \vee \neg q\) are equivalent.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the following propositions.</span></p>
<p><span>\(p:{\text{ Amy eats sweets}}\)</span></p>
<p><span> \(q:{\text{ Amy goes swimming.}}\)</span></p>
<p><span>Write, in symbolic form, the following proposition.</span></p>
<p><span><em>Amy either eats sweets or goes swimming, but not both.</em></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider each of the following statements</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\[p:Alex{\text{ }}is{\text{ }}from{\text{ }}Uruguay\]\[q:Alex{\text{ }}is{\text{ }}a{\text{ }}scientist\]\[r:Alex{\text{ }}plays{\text{ }}the{\text{ }}flute\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the following argument in words</span><br><span>\[\neg r \Rightarrow (q \vee p)\]</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table for the argument in part (a) using the values below for \(p\) , \(q\) , \(r\) and \(\neg r\).</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The argument \(\neg r \Rightarrow (q \vee p)\) is invalid. State the reason for this.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The probability that it will snow tomorrow is 0.3.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If it snows tomorrow the probability that Chuck will be late for school is 0.8.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If it does not snow tomorrow the probability that Chuck will be late for school is 0.1.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that it does not snow tomorrow and Chuck is late for school.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Chuck is late for school.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A fitness club has 60 members. 35 of the members attend the club’s aerobics course (<em>A</em>) and 28 members attend the club’s yoga course (<em>Y</em>). 17 members attend both courses. </span><span style="font-family: times new roman,times; font-size: medium;">A Venn diagram is used to illustrate this situation.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>q</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>p</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of members of the fitness club who attend neither the aerobics course (<em>A</em>) nor the yoga course (<em>Y</em>).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Shade, on your Venn diagram, \(A' \cap Y\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table below.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether the statement \((p \wedge q) \Rightarrow (\neg p \underline \vee q)\) is a logical contradiction, a tautology or neither.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Give a reason for your answer to part (b)(i).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A group of 30 students were asked about their favourite topping for toast.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> 18 liked peanut butter (<em>A</em>)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> 10 liked jam (<em>B</em>)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> 6 liked neither</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show this information on the Venn diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of students who like both peanut butter and jam.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that a randomly chosen student from the group likes peanut butter, given that they like jam.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Merryn plans to travel to a concert tomorrow. Due to bad weather, there is a 60 % chance that all flights will be cancelled tomorrow. If the flights are cancelled Merryn will travel by car.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If she travels by plane the probability that she <strong>will be late</strong> for the concert is 10 %.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If she travels by car, the probability that she <strong>will not be late</strong> for the concert is 25 %.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram below.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Merryn will not be late for the concert.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Merryn was not late for the concert the next day.</span></p>
<p><span>Given that, find the probability that she travelled to the concert by car.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">\(U = \{ x|x{\text{ is an integer, }}2 < x < 10\}\)</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><em>A</em> and <em>B</em> are subsets of <em>U</em> such that <em>A</em> = {multiples of 3}, <em>B</em> = {factors of 24}.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of</span></p>
<p><span>(i) <em>U</em> ;</span></p>
<p><span>(ii) <em>B</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the elements of <em>U</em> on the Venn diagram.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(n (A \cap B)\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">When Andy plays tennis, \(65\% \) of his first serves go into the correct area of the court.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">If the first serve goes into the correct area, his chance of winning the point is \(90\% \).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">If his first serve does not go into the correct area, Andy is allowed a second serve and, of these, \(80\% \) go into the correct area.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">If the second serve goes into the correct area, his chance of winning the point is \(60\% \).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">If neither serve goes into the correct area, Andy loses the point.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Andy loses the point.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following histogram shows the weights of a number of frozen chickens in a supermarket. The weights are grouped such that \(1 \leqslant {\text{weight}} < 2\), \(2 \leqslant {\text{weight}} < 3\) and so on.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the total number of chickens.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the modal group.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Gabriel chooses a chicken at random. </span></p>
<p><span>Find the probability that this chicken weighs less than \(4{\text{ kg}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p><span>The sets \(P\), \(Q\) and \(U\) are defined as</span></p>
<p><span><span><em>U</em> = {Real Numbers} , <em>P</em> = {Positive Numbers} and <em>Q</em> = {Rational Numbers}.</span></span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down in the correct region on the Venn diagram the numbers</span></p>
<p><span>\(\frac{{22}}{7}\) , \(5 \times {10^{ - 2}}\) , \(\sin (60^\circ )\) , \(0\) , \(\sqrt[3]{{ - 8}}\) , \( - \pi \).</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Music lessons in Piano (<em>P</em>), Violin (<em>V</em>) and Flute (<em>F</em>) are offered to students at a school. </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The Venn diagram shows the number of students who learn each kind of instrument.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the total number of students in the school.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of students who</span></p>
<p><span>(i) learn violin only;</span></p>
<p><span>(ii) learn piano or flute or both;</span></p>
<p><span>(iii) do not learn flute.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Explain, in words, the meaning of the part of the diagram that represents the set \(P \cap F'\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In an international competition, participants can answer questions in <strong>only one</strong> of the three following languages: Portuguese, Mandarin or Hindi. 80 participants took part in the competition. The number of participants answering in Portuguese, Mandarin or Hindi is shown in the table.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>A boy is chosen at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the number of boys who answered questions in Portuguese.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the boy answered questions in Hindi.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two girls are selected at random.</p>
<p>Calculate the probability that one girl answered questions in Mandarin and the other answered questions in Hindi.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Maria travels to school either by walking or by bicycle. The probability she cycles to </span><span style="font-family: times new roman,times; font-size: medium;">school is 0.75.</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">If she walks, the probability that she is late for school is 0.1.</span><br><span style="font-family: times new roman,times; font-size: medium;">If she cycles, the probability that she is late for school is 0.05.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram below, showing the appropriate probabilities.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Maria is late for school.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following propositions.</p>
<p style="padding-left: 90px;"><br><em>p</em>: my Mathematical Studies homework is due tomorrow<br><em>q</em>: today is Wednesday</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down in words the compound proposition <em>¬</em>\(p \Rightarrow q\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the truth table.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether the compound proposition (\(\neg p \Rightarrow q\)) ∨ (\(\neg p \wedge q\)) is a tautology, contradiction or neither.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p><span>The Venn diagram shows the number sets \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and \(\mathbb{R}\). Place each of the following</span> <span>numbers in the appropriate region of the Venn diagram.</span></p>
<p><span>\(\frac{{1}}{{4}}\), −3, π, cos 120°, 2.7 × 10<sup>3</sup>, 3.4 × 10<sup>–2</sup></span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The grades obtained by a group of \(20\) IB students are listed below:</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the following table for the grades obtained by the students.</span></p>
<p><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL8AAADTCAIAAABfvlVwAAAMnUlEQVR4nO2dzWsbRx/H+5+sYE8SCFJy0cmnHlQfhDA9POBLiyxQDnnwA4U+IOHwPPRQCEhYFAK5rLAJhEC6wqUNBJfFUEJQ2UMhBzHQB0wRSzEPZlkehDDDPId904tXtn/SZHbl74c5JF5bmhl9dua3o3n5RABA5RPVGQAZBvYAOrAH0JmxR9dySEjLU6I9vkDSjZXMBhQhtcAeQAf2ADqwB9CBPYAO7AF0VrfHZZbZa1bCR7hSvf3KYq5wf+2d/LmOHP7Zr30avPiDtn1157+/sz1XdufBkmfUx33n7pnYUFayhzvvurWSrpXq7bfM40IIISaObXZqJV37tG6uxR4hxJgZux/PHiGE4K51UNRyupZ7GL/nxLFftMr7sCdiBXu8Qadc0LXCdnvgzV3i5/3GZ+uz58oxH39ce8SV3X44b48QQnD26xnsCSHbE7YH2m6PjRcv89FP3fX0XCId9oyZ9d4hvNBGQ7WHD3uVgq7l9IrB+LI3iD4G/UHbvmS/tPeK2lbLuhBCCOEy61WnVtK1nK4VtpsvbGcS/p3fTRR0rbDdfGUZjXl7PP+lcrpWaR0NnOQ8rMOeiTN4Vm+YzsLVawqVmDHusbdBYfN73cFweNr9+6F9Fd0bQQHjOG+q2Zv623Lz2Ha4mI7PPn9qnh77oWf5oM/cuBhxZsLqdcz6XAwX/IQSaVDtiTJRM2+6I8NWKr/bev27y4xqUC/+z7da1oXg5/1GadpFzoyqltPzB5bLw+hqyh7vQ69W0vP7/dGEM6OqlR6Z50n+rGhPnGZKmlCoxIxxz+5ua7li7XjoXfn/nvLDs9ufxwV0rVZ++ir3hsf1fK7YMEd8zIxd//XjWtIK2wenDr+wmlsz+fQzo+322P+CMK5iMB68mq4VqsaQB4V99o/kClzCR7Anurd2e2ws+LBX+axlXQgxGZn7RS1XbFruXPWJoCKKTcudfoXgahjS+m/t34LJnZqMtiehUH8lZixoqsP2KWw2rrdn/qpfG0Hb4GcsuBR8Cp93bG/+RaJa8m9Ib9ApF4oNc8TFlPoHlsuFuLSPflregSRBtSe8P2Z6rplWMXIrrOggr3Nwj1m99net6dYl7BbD6puzJ6ym2z1Iy4l7ri1UcsZmPuY72nPtCIIv6DJ7wv9ee3sHH1+hagy5+75/dkGoIrFC1By2k/NORNF01DAmx7x+r5zf74/+u/TmS7DnppDrpiIsI+mZK7p+XaESMxa+2ir2xB1NzDJ7wg/o+lY5/JjK3/1w9PLsmrv6VtCf2Llz+qRcWChV1KRHUViSPZd2e0e/U88VmBo1vEH3f6cS3hKSPckZC+71pJ5rdkBr7mrYEof9zhTL7Ilu452OfblYAD4yH+UTpLw1dHtELFClZVjhaGGU6ejBaq6XDYka5IrBXH/oKO6zg7jSDz+ds27ts+kWOyy5H4RywR37JzvpsYtkTzxaGBo8x/WFSs5YeKs0zFEct8ZxcfB2+QPLHTvWt7MxdRAg6lqpbnzwhOCO/bPt8Dhq9qt6obEJBuRyxdqz35yJEC6zfg0/pihL1w+43JKV7BFCCO7YJy/Dp+6cruX0crNnvomevWcfXqajE3doNIr+71sfWFBllZY59IQQwmWn3Xo+p2ul+uGZ/fqbevtl/yRSZOoJdmak++YS3sw1cUbY48S/klSo5IxFD8/5ve478+lM2yOEN+z7j9xTV6feN6qNnJ7f65wybz6fe5323nxUJAR3BsGTvFaqt82pAREhhODM+GKxPbsLK9uTetJYhPmeSxErxMs+sEcFKu2ZjMz9Yrlre+PRyStyvOwDe1QQjnckBFVS8ceyH/fZ+55hz39BeUdgz0dndlTsozc/Ez8qD+L61YA9gA7sAXSW2bMw6I6ENJ8S7VmUK4tsQBFSC+wBdGAPoAN7AB3YA+jAHkBHoT0us05+aO89lDxaD3vkocqeMTMaX9X+VpT/XQ/skYfSnosPe5UC7MkusAfQgT2ADuwBdGAPoAN7AB3YA+jAHkAH9gA6quyJF2vqWm7FFY3LgT3ywLekgA7sAXRgD6ADewAd2APowB5AZ5k9yleaIaU/JdqzKFcW2YAipBbYA+jAHkAH9gA6sAfQgT2Ajip7praQjQ59kQPskYcSeyajk2ddf9Nh7vx2uFdM2M98LcAeeaiwh//n7OzPqQ3W5c4Rgz3ySEPcc2E1t2BPFkmJPZUlx7OtCOyRRwrsca1WpWuvvHdwErBHHsrtubTbX8sLmQXskYlae7hnP28ZH1bc7345sEceKu3hozfdI7nqCNgjE2X2cMfqHlrxeVvD173VTvtJAvbIQ4k93GNmyz8MME6ylnTBHnkosCc6fnEm3e6IWgKwRx7Kn7mkswFFSC2wB9CBPYAO7AF0YA+gA3sAnWX2KF9phpT+lGjPolxZZAOKkFpgD6ADewAd2APowB5AB/YAOsrs4c67bq2kazm9fNBnEndszoI93GNvO35taJXW0UDi4si1osge7/f+0XuHh6sB8weWe39nxfPRm+7hW+ZxISbO4Fk9X9huD2RPuVwLSuwZ/3H2fhTZ4lqt/FbLkjKxUGTAntnaEGNm7Ooyb6c1oj7u4cyolrEiJ4K71oHUxniNqLXHZZbRqn1nORN575FFex42zFEG5FFoj2u1gvmplZY5lNfNZ82eC6u5J3WB2xpR3HNxZ3DcrOhaCSuRhRBCcM/+vp6RkFkot0cI7KExhTfoNl8MpYWAaycF9ogxM3Zhj+DnPx6+ypA6Ih32YA8NIfjIOnwePz14H46Nd1IPvVsLKuzh5/3G1nbzhe1MhJg41rfV2rG8ey4D9njDfrMyO+uqUDWG6W+FlLQ97tBoBAcD5vc6psxdC9NvDz/vN0oLc/YkHpa4RtLQc8llA4qQWmAPoAN7AB3YA+jAHkAH9gA6y+xRvtIMKf0p0Z5FubLIBhQhtcAeQAf2ADqwB9CBPYAO7AF01NvDR+ajvMSvlGGPPFTbE8xPgD2ZRK09l3Z7/5/NL4uwJ5sotMdfP/B+ZB3Anoyizh5v0Kl9b3tXLuzJLKrsiQ5147Anuyixh3v28yfBIgrYk2FU2OMNugcn4Tpt2JNhPr49vi7Xfd0v55Al2CMP1eM9aHuyDOwBdGAPoKPcHulsQBFSC+wBdGAPoAN7AB3YA+jAHkBnmT3KV5ohpT8l2rMoVxbZgCKkFtgD6MAeQAf2ADqwB9CBPYCOQntmp4nJmRomMmcPP+83tjKxWbNQac/MPsUSN7fOlD2TkblfzMhW30KdPdyzu1VpZ1NMkx17uGd/X//mm3oe9tzAhdXc0rVKyzAtmUfaigzZ4y9wG522YM9yODOq8Wg3TncT8QI314I9t4I79o9Gc1vL6dqOvNPwsmDP1KFusOdOcOf0Sfl+n+42vcAN9twRuacAp96eS/vwaX8UnswFe+4KZ0b13o73xKf7zqUMHLKUBnu4az19Yl1IevW02zMH2p6bmDj2mx+DM90mzuB561+n8g54gz3yUGSP9e22ltO1XLHW/sFiUg+Qhj3ySEPPJZcNKEJqgT2ADuwBdGAPoAN7AB3YA+gss0f5SjOk9KdEexblyiIbUITUAnsAHdgD6MAeQAf2ADqwB9BRbQ937JOXnVpJ17Zacqb4wB55qLSHO++6tZLsSRqwRx7q7PEGnfJW/fCdvHlhPrBHHqrsubTbO8WGOZI/CQr2yEONPZwZVa3SMl50aiVdyxVr3V+krSiFPfJQYs+YGbt6uXnsT232PvRqJb3ctb37uSInwyix58Jqbk0v/+PMqErbOAL2yEOFPXzYq8wuHl38yfqAPfJQ1vbMbPfEh73Kp2h7MocSe/ylx/uzy29lLZ2EPfJQ9MTOz/uNUrF2PPS44M5vh42qv4OEBGCPPBSOFrJf2ntFLadrldbRAGtJs4jq77nkswFFSC2wB9CBPYAO7AF0YA+gA3sAnWX2KF9phpT+lGjPolxZZAOKkFpgD6ADewAd2APowB5AB/YAOorsuWaD9Hs+M5V77Kz/ul1/IOvEBRkosWf2TMkg3evZYZwZX3y591U+p0s7r0MGSuy5sNpdy5nEP3Ct1s59PaciZsyMXdhzE/wv9sf0/PcxM77EuaSwhwQf9na+juc4rxvYIw/19nBmfCHzeFvYIw/l9oyZ8VjS3is+sEcequ3hw97Ov6XWF+yRh2J7ZHdbAvbIRK090rstAXtkotQe+d2WgD0yUWkPZ8ePpC0hjciGPTNf3eBswNSwAUVILbAH0IE9gA7sAXRgD6ADewCdZfYoX2mGlP6UaA8AdwL2ADqwB9CBPYAO7AF0YA+g83/xQhlEAe9QEQAAAABJRU5ErkJggg==" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the modal grade obtained by the students.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the median grade obtained by the students.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One student is chosen at random from the group. </span></p>
<p><span>Find the probability that this student obtained either grade \(4\) or grade \(5\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The probability that Tanay eats lunch in the school cafeteria is \(\frac{3}{5}\)</span><span style="font-size: medium; font-family: times new roman,times;">.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If he eats lunch in the school cafeteria, the probability that he has a sandwich is \(\frac{3}{{10}}\)</span><span style="font-size: medium; font-family: times new roman,times;">.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If he does not eat lunch in the school cafeteria the probability that he has a sandwich</span> <span style="font-size: medium; font-family: times new roman,times;">is \(\frac{9}{{10}}\)</span><span style="font-size: medium; font-family: times new roman,times;">.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram below.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Tanay has a sandwich for his lunch.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">\(U\) is the set of all the <strong>positive</strong> integers less than or equal to \(12\).</span><br><span style="font-size: medium; font-family: times new roman,times;">\(A\) , \(B\) and \(C\) are subsets of \(U\) .</span><br><span style="font-size: medium; font-family: times new roman,times;">\[A = \{ 1{\text{, }}2{\text{, }}3{\text{, }}4{\text{, }}6{\text{, }}12\} \]</span><span style="font-size: medium; font-family: times new roman,times;">\[B = \{ {\text{odd integers}}\} \]</span><span style="font-size: medium; font-family: times new roman,times;">\[C = \{ 5{\text{, }}6{\text{, }}8\} \]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of elements in \(A \cap C\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of \(B\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the following Venn diagram with <strong>all</strong> the elements of \(U\) .</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The probability that it rains today is \(0.4\) . If it rains today, the probability that it will rain tomorrow is \(0.8\) . If it does not rain today, the probability that it will rain tomorrow is \(0.7\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the probability of rain tomorrow.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A school offers three activities, basketball (<em>B</em>), choir (<em>C</em>) and drama (<em>D</em>). Every student must participate in at least one activity.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">16 students play basketball only.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">18 students play basketball and sing in the choir but do not do drama.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">34 students play basketball and do drama but do not sing in the choir.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">27 students are in the choir and do drama but do not play basketball.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Enter the above information on the Venn diagram below.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>99 of the students play basketball, 88 sing in the choir and 110 do drama.</span></p>
<p><span>Calculate the number of students <em>x</em> participating in all three activities.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>99 of the students play basketball, 88 sing in the choir and 110 do drama.</span></span></p>
<p><span>Calculate the total number of students in the school.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Shade \((A \cup B) \cap C'\) on the diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>In the Venn diagram below, the number of elements in each region is given.</span></p>
<p><span>Find \(n((P \cap Q) \cup R)\).</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(U\) is the set of positive integers, \({\mathbb{Z}^ + }\).</span></p>
<p><span>\(E\) is the set of even numbers.</span></p>
<p><span>\(M\) is the set of multiples of \(3\).</span></p>
<p><span>(i) List the first six elements of the set \(M\).</span></p>
<p><span>(ii) List the first six elements of the set \(E' \cap M\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The table below shows the number of words in the extended essays of an IB class.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a histogram on the grid below for the data in this table.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the modal group.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The maximum word count is \(4000\) words.<br></span></p>
<p><span>Write down the probability that a student chosen at random is on or over the word count.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following Venn diagrams.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in set notation, for the <strong>shaded</strong> region represented by Diagram 1.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in set notation, for the <strong>shaded</strong> region represented by Diagram 2.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in set notation, for the shaded region represented by Diagram 3.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Shade, on the Venn diagram, the region represented by the set \(\left( {H \cup I} \right)'\).</p>
<p><img 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"></p>
<p> </p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Shade, on the Venn diagram, the region represented by the set \(J \cap K\).</p>
<p><img 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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>All the children in a summer camp play at least one sport, from a choice of football (\(F\)) or basketball (\(B\)). 15 children play both sports.</p>
<p>The number of children who play only football is double the number of children who play only basketball.</p>
<p>Let \(x\) be the number of children who play only football.</p>
</div>
<div class="specification">
<p>There are 120 children in the summer camp.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in terms of \(x\), for the number of children who play only basketball.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the Venn diagram using the above information.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of children who play only football.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of \(n(F)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The probability that Nikita wins a tennis match depends on the surface of the tennis court on which she is playing. The probability that she plays on a grass court is \(0.4\). The probability that Nikita wins on a grass court is \(0.35\). The probability that Nikita wins when the court is not grass is \(0.25\).</p>
<p>Complete the following tree diagram.</p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Nikita wins a match.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 60 sports enthusiasts visited the PyeongChang 2018 Winter Olympic games to watch a variety of sporting events.</p>
<p>The most popular sports were snowboarding (<em>S</em>), figure skating (<em>F</em>) and ice hockey (<em>H</em>).</p>
<p>For this group of 60 people:</p>
<p style="padding-left: 120px;">4 did not watch any of the most popular sports,<br><em>x</em> watched all three of the most popular sports,<br>9 watched snowboarding only,<br>11 watched figure skating only,<br>15 watched ice hockey only,<br>7 watched snowboarding and figure skating,<br>13 watched figure skating and ice hockey,<br>11 watched snowboarding and ice hockey.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the Venn diagram using the given information.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxMAAAHFCAYAAACJoqRLAAAgAElEQVR4Ae3dD7BW9Z3n+e9N3JmFODairkoDQbQBbUaQIKEXGGibXMTYC4uyXTI0OhGdlINO2dWgg6SECbAKVtMNhHUAU0hY2TTxFlTbIoSw2MAMQUQwbBA6KggBXRQJzWBvl83d+hxz8OHc+zz3+XP+/H7nvE9Vwr3Pc/78fq/vEX7f8/tzmlpbW1uNDQEEEEAAAQQQQAABBBCoUeArNe7P7ggggAACCCCAAAIIIIBAIHBZ1KGpqSn6Eb8jgAACCCCAAAIIIIAAAoFA6cCmNsmE9ijdATMEEEAAAQQQQAABBBBAQALRjgeGOXFfIIAAAggggAACCCCAQF0CJBN1sXEQAggggAACCCCAAAIIkExwDyCAAAIIIIAAAggggEBdAiQTdbFxEAIIIIAAAggggAACCJBMcA8ggAACCCCAAAIIIIBAXQIkE3WxcRACCCCAAAIIIIAAAgiQTHAPIIAAAggggAACCCCAQF0CJBN1sXEQAggggAACCCCAAAIIkExwDyCAAAIIIIAAAggggEBdAiQTdbFxEAIIIIAAAggggAACCJBMcA8ggAACCCCAAAIIIIBAXQIkE3WxcRACCCCAAAIIIIAAAgiQTHAPIIAAAggggAACCCCAQF0CJBN1sXEQAggggAACCCCAAAIIkExwDyCAAAIIIIAAAggggEBdAiQTdbFxEAIIIIAAAggggAACCJBMcA8ggAACCCCAAAIIIIBAXQIkE3WxcRACCCCAAAIIIIAAAgiQTHAPIIAAAggggAACCCCAQF0CJBN1sXEQAggggAACCCCAAAIIkExwDyCAAAIIIIAAAggggEBdAiQTdbFxEAIIIIAAAggggAACCJBMcA8ggAACCCCAAAIIIIBAXQIkE3WxcRACCCCAAAIIIIAAAghcBgECcQk0NTXFdSrOgwACCCCAAAIFFmhtbS1w7f2qOsmEX/FyvrT8x+98iCggAggggAACTgvwcNLp8LQpHMOc2pDwAQIIIIAAAggggAACCFQjQDJRjRL7IIAAAggggAACCCCAQBsBkok2JDn84PM37bmbmkzdhl/+7w/tuTfPXazs528+ZzeVfH/Tc2/a5xe/5QcEEEAAAQQQQAABBNoKNLVGBrmrsRn5qO1RfOKhwD/a4R9Osb4PHrQpL6y1H3ynv10eqcWFX7fYQyO32rdf/wub8Lv/IvJtx79y73RsxB4IIIAAAgggUFmA9kRln6y/jcaHnomsI5L29a//Y7v/3lvaJBJBMf77P9j/MHOaja8jkUi7GlwPAQQQQAABBBBAIHsBkonsY5BOCS4csR0/3mH2rcF28xXthf0f7Vc7/pv9Tq+rrb1v0ykkV0EAAQQQQAABBBDwSYB2o0/RaqCsF371X+3Hm82aR95i17Z7nnN2/Fe9bMzgru1+y4cIIIAAAggggAACCEQFSCaiIrn8/YKdO/4r+4X1tW8N6N5+z8PZt23T2/+Tdb+cWyKXtwCVQgABBBBAAAEEEhCg5ZgAqnunPG17Nm22k9f/gQ36vc7tFO+Cnd2zzf6fCf+z3cQd0Y4PHyGAAAIIIIAAAgi0J0DTsT2VvH32+VHb+/KbFeZLnLW/3/v/2qhyvRZ586A+CCCAAAIIIIAAArEIkEzEwuj4SU4dtV+8a3bjv/66XdNeUc/utb9+vmuZXov2DuAzBBBAAAEEEEAAAQSs/eHzwORM4Gtd7Lrrzc6f+o2db1O1M/bm8iW2+7vjbUi7qzy1OYAPEEAAAQQQQAABBBAIBOiZKMKNcMVg+3dzv2O24Fmb9+JuO3nhi0pfOPmmtTz3H+2P//bf2HPfHdz+uyeK4EMdEUAAAQQQQAABBOoSIJmoi823g66wft9ZZNt+9idmq8Zbt682md5e+NVvLLb3ev072/Y3/9G+wSpOvgWV8iKAAAIIIIAAApkLNLW2traWliL6iuzS7/gZgUoC3DuVdPgOAQQQQAABBKoRoD1RjVJ2+0TjQ89EdrHgyggggAACCCCAAAIIeC1AMuF1+Cg8AggggAACCCCAAALZCZBMZGfPlRFAAAEEEEAAAQQQ8FqAZMLr8FF4BBBAAAEEEEAAAQSyEyCZyM6eKyOAAAIIIIAAAggg4LUAyYTX4aPwCCCAAAIIIIAAAghkJ0AykZ09V0YAAQQQQAABBBBAwGsBkgmvw0fhEUAAAQQQQAABBBDIToBkIjt7rowAAggggAACCCCAgNcCJBNeh4/CI4AAAggggAACCCCQnQDJRHb2XBkBBBBAAAEEEEAAAa8FSCa8Dh+FRwABBBBAAAEEEEAgOwGSiezsuTICCCCAAAIIIIAAAl4LXOZ16Sk8AgggkLLAZ599ZseOHavpqldffbV17dq1pmPYOX8Chw8frqlSnTt3tu7du9d0DDsjgAACaQuQTKQtzvUQQMBJgTBJOHXqlH300Ud24sQJ++CDD4Kybtu2zd54442L5Z4+ffrFn6v5odzxXbp0sX79+tnll19uvXr1MpKOajTd20dJwvnz5+29996zc+fO2YEDB4JC6vMNGzZcLPDUqVPtyiuvvPh7Rz+UOz68b3R8//79jaSjI0m+RwCBJAWaWltbW0sv0NTUZJGPSr/mZwTKCnDvlKXhC8cE1Eg7cuSI6U8lDAsXLgxKqCQh2lDTF3E28sOkRedVGdT4DBOXMOlQo/OGG24IEg01FuO8vmOh8Ko4ul+UbL777rtBwlAaLyUJQ4cODerTu3fvoIEfdyNf19cWJrxh4qLPlbSMGzfO+vTpE5RDZdB9Q8+GV7cYhf2tAO0Jt2+FaHxIJtyOl1eli95cXhWewuZW4Pjx43b06FF76623bP/+/bZy5UpTY33AgAFBw0s9Aj169LBOnTo5YxBttCrZUUNxyJAhNnjw4KAXQ41GtuQETp8+HSSab7/9dpA4lMZAvUkuJnnhva6etV27dpmSHW2jRo0KEgyV2bV7PbkIcmafBWhPuB29aHxIJtyOl1eli95cXhWewuZGQI3AgwcP2uuvv27r168P6jV+/HjvG+FhQ1FJ0ZYtW4In0epJGT16tN1yyy08gW7wDlaP0aFDh2zHjh2X+Kq3wedGeGlStH379ovJ9IgRI4IEg6S0wRuHwxMRoD2RCGtsJ43Gh2QiNlpOFL25EEEgLQE1tLdu3WphY2nevHlB8pDnRnaYNIXJhayVWAwfPtwGDhyYFr3X15Hhnj17guRBPQ9KzsLkIa+N7DBpUo9LS0tLMMROyfbIkSNt0KBBTvXQeX1zUfiGBGhPNMSX+MHR+JBMJE5enAtEb67i1JyaZiGgoUCbN2+21atXW7du3WzChAl26623FrYhrYRq9+7dtnHjxuDpsxIqGoht78ww8Qwb0lOmTLHbbrutsA3pMKFSUvXUU08FCZWSUvVcuDT0r20k+STPArQn3I5uND4kE27Hy6vSRW8urwpPYb0QKG0IqsBKIO644w6G+ESiFzYQ161bF8wTUYO5yD0WeERukDK/qtdi7969wRBBJRYkpGWg+DhxAdoTiRM3dIFofEgmGuLk4FKB6M1V+h0/I1CvQNjAWbVq1cWGsYZlsEpNdaJqSGsirnpwtCmx0ITcIrz3Yt++ffbqq68GT9zVML7rrrsK23NV3d3y5V78d/elBT+lL0B7In3zWq4YjQ/JRC167FtRIHpzVdyZLxHoQECN4JdeeiloBKvxq9WMhg0b1sFRfF1JIBwa9uijjwZPne+9995gRatKx/j2nRrBGuoVJk+PPPIIQ3YaDKL+W3zllVds6dKlwSpoDzzwAP8tNmjK4ZUFaE9U9sn622h8SCayjkiOrh+9uXJUNaqSooAavFq+VU/T9RR90qRJhXiKniKxRRvcmnjse6IWJp95TpTSvEfKXWvnzp0W9hI++eSTNnbsWOZWlMPi87oFaE/UTZfKgdH4kEykwl6Mi0RvrmLUmlrGJaBGSvjyOJ4mx6Xa8XnkrheeKXnzsXFYmnxOmzbN7r77bpLPjsPe8B6lvVxLliwh6W9YlBOUCtCeKNVw7+dofEgm3IuRtyWK3lzeVoSCpypQmkTk4Ql5qngxXqy0Ue5DUuFbeWMMlVOnKu0RIqlwKjReF4b2hNvhi8aHZMLteHlVuujN5VXhKWzqAiQRqZNXdUHXG+mul68q5BzuRFKRw6BmWCXaExniV3HpaHxIJqpAY5fqBKI3V3VHsVfRBMLGoP6kJ8Ld6Idx0vCnRYsWZT6nQo3V559/PniruQ89J+5GNtmShUmFJsATp2St83x22hNuRzcaH5IJt+PlVemiN5dXhaewiQuokfHMM88EY/Pnzp1rzc3NiV+TCzQuoKRixowZwYkWLFiQ+upPmiyu92Xcf//99uKLL9rEiROZ8Nt4WBM/A/+9J06c6wvQnnA7vNH4kEy4HS+vShe9ubwqPIVNTCBcOeiee+6hMZiYcvIn1rC0xx9/3PSOj+9+97upTHLO4prJSxbrCmEyes011wQ9kX369CkWALWtS4D2RF1sqR0UjQ/JRGr0+b9Q9ObKf42pYUcCemnY7Nmzg6fZGvJQhBeldWTi8/dhL4HeN6B46g3kSWx60/nixYtNDdEsekOSqFPRz7l582abNWtWsNzzgw8+SO9S0W+IDupPe6IDoIy/jsaHZCLjgOTp8tGbK091oy61CajRqXH269evt+XLl/PW4dr4nN9bjf05c+YE5dS8l7ieNpf2Yr388suJJSvOA+e0gPy9kNPAJlAt2hMJoMZ4ymh8vhLjuTkVAgggYHoCOXLkSOvevbu9/vrrJBI5vCcU2xUrVgTzFyZPnhy8bVoNxUY29ULcd999tmvXLvvkk09IJBrBdPTYTp062cyZM23NmjVBj6Xm4mhuBRsCCPgtQM+E3/FzqvTRTNWpwlGYxAXCp467d+9maEri2u5cIJxoq2RAw5+UaNS6aeUfHcvE/Frl/N1ff19oYr3iTu+lv3FMquS0J5KSjee80fiQTMTjylnMLHpzgVIcAc2NePjhhxkPXZyQt6mpeqTGjBljtQxPKh0u9eyzzzKnpo1q/j9QEqreLU3s1wR/9V6wIUB7wu17IBofhjm5HS9Kh4DzAnqqrERCTxenTZtGY8D5iCVTQC31e+zYMdu4cWOwlGxHw1eUfGgC99ixY4MhU0zOTyYurp9V8200HFKbhrkpwWRDAAG/BOiZ8CteTpc2mqk6XVgK17CAGotPPPFEcB6eKjfMmZsTdDR8heFwuQl17BUJe7c2bdrEe2hi1/XrhLQn3I5XND70TLgdL0qHgJMCGtZ055132ogRI3iq7GSEsiuUhqlMmTIl6KlSj1VLS8vFwuip82OPPRb8vnbt2thWgbp4AX7wWiDs3Vq2bJnNnz/flHiyIYCA+wL0TLgfI29KGM1UvSk4Ba1JQI1DvcmaSZM1sRVy53BOxA033GBDhw4N3k2R5PspComcw0qHvVfvv/++Pf3003VN6s8hS6GqRHvC7XBH40My4Xa8vCpd9ObyqvAUtkMB/oHvkIgd2hHQfTN16lT76U9/aj/60Y+CSdrt7MZHCLQR4MFFG5LCfEB7wu1QR+PDMCe340XpEHBCQA1CDU85c+ZM8Gbiepb/dKIiFCJVAd03L7zwgnXu3NnmzZtn3/ve94K3WqdaCC7mrYAm6Ovllxout3PnTm/rQcERyLsAPRN5j3CK9YtmqilemkslKKChKvpHXePgtVoTGwLVCIQJqPZdvHhxsMqXGoTDhw+3HTt22LBhw6o5DfsgEKzwxN9BxboRaE+4He9ofOiZcDtelA6BTAW0Bnz4dJBEItNQeHXxcKL1gAEDggn64bsDlEBo+Vi9T6B0YrZXlaOwqQuoJ1TLx+7fvz94yZ0SVTYEEHBHgJ4Jd2LhfUmimar3FSp4BXiKXPAboM7qV9OTVc0+dV6ew3Is0F5vV46rW+iq0Z5wO/zR+NAz4Xa8KB0CmQgokdDT40OHDjEcJZMI+HnRMEnQOPdKPVnRJ81+1pZSpy2gHi4NmVOPl+Zw0UORdgS4HgLtC9Az0b4Ln9YhEM1U6zgFhzggECYSGobCRGsHAuJJEUoTiWrnQ4RPmtU4rJR8eEJAMVMUWLp0aTDsKZyPk+KluVQKArQnUkBu4BLR+NAz0QAmhyKQNwESibxFNJ361JNIqGThk+ZwLHw6peUqeRBQ8kkPRR4iSR3yIEAykYcoUgcEYhAgkYgBsYCnqDeRCKlIKEIJ/qxVgISiVjH2RyAZAZKJZFw5KwK1CVw4aW+++IT9YVOTqfuw6Q+fsB9uPWxnD//IZrYcq+1cdexNIlEHGodcXLJTcySqHdrUHhsJRXsqfFaNQJYJxedvPmc3hX9nl/1zsD2x9eNqqsI+CHgrQDLhbegoeH4Eztibf/GQDV71VXv00G+stbXV/vmle+yrmx613+n7N3ZT/2sSrSqJRKK8uT15oz0SURgSiqgIv1crkFVCcdk3/tx+9Zuf2YzrzWzKy3aitTX4+1t/h7e2/rP9w8FVNuXGZhszuGu1VWE/BLwUIJnwMmwUOlcCn79r//fzf2s3fvse+1/6XBFU7SvXD7H7n3rCZvQfYgN6/4+JVZdEIjHaXJ847kQixCKhCCX4s1aBrBKKCx8esX0nr7fmkbfYtZcU+it2eZ9v2h3/odkGX0FT6xIafsmdAHd47kJKhXwVOH/wqH10oaT0nX/HrvtfB9nvXVbyWYw/qkGo5V81RIVVm2KEzfmptALTnDlzgtWXGhnaVI5JCcWzzz5rq1evNiW7bAhUK/Dggw8Gu77wwgvVHtLgfhfs3PFf2S9suP3J8F72RYPqgp3dusgWvXnO7Cv97P7HR9kXj4gavBSHI+CwAMmEw8GhaAURuOxG+8PvfttO/nCaTf5PLXb43G8zisu+YY//5zsS+YcoqSfLBYlYYatZupTrlClTEnPo2rVr8IZsJbskFIkx5+7E6fdsnbY9mzbbyeY7bfhN6kG+YOcOr7d5z35qA36vc+58qRAC5QRIJsrJ8DkCqQl0sW/82Qr7+V98yw4tuMdG/Yf/w3af/KfErp70k+XECs6JMxfQE98rr7wylXdCqLdszZo1Qe+Zkl82BKoRSLVn68LHdmTfCbPND1rfr2rxjK/av+p7jy2wXtb9cppX1cSLffIhwN2ejzhSC98FvnK9DXl8iW194Ttmq6fZNyf977Y1oYTi6aefDtZnT/LJsu/hoPxtBTTsSO+D0BCntLY+ffoEw/AmTJhgp0+fTuuyXMdzgdKercOHDydWmwu/+q/2481mzS8ctH8OJl3/f3biZ7Pt298aYL1pXSXmzondE+B2dy8mlKiwAldYv+8sChKK67fNtsl/ucPOxmyht8Z++umnFo4tjvn0nC6nAhpqpHtHiaie/Ka5aV6GEt8nnnjC1KvGhkA1AurZ0nywyZMnB0sYV3NMbft8bh8d2G2bra99a0D3386X+Bd2bfd+9keDvm4JTXWrrYjsjUBKAiQTKUFzGQTaCmii3gp78fA/lnx1hfW799/an15vdvLlvfb3n5d81eCPahDq6bImt6bdIGyw6ByeoUA4UV9DjrKaqK+VejS8Kr2JtRmCc+nYBJSI6t5Rb1r8iegZO/jzPWbX/4ENKpkf8ZU+f2KP33F1bHXgRAj4IEAy4UOUKGNOBTR5b4P98vi5dut3/T3xreRU2iDUEAA2BKoRUANMjbG5c+eahhxlualBuGXLFtu8eXOWxeDangmoVyuRRPTs27bpR2+afWuw3czSr57dFRQ3bgGSibhFOR8C1QoEk/f22oLvL7QX3zxpwRpO596xlnnP2oKT37Y/+98GxbKSk0sNwmpp2M8NAQ0TGTJkiDU3N2deIPWmaajVmDFjEhq2knkVKUBCAvEnov9kv97SYj86eaNNGXe76Z11bAgUWYBkosjRp+6ZClz41V478u932m/+yxj7579+wL7a1GRN/+pmm/bhnbb50Ev259/oEkv5XGoQxlIhTpKKgHoAdu/eHaymlMoFq7iIhllt2rQp6C2Jf9hKFQVgFy8FYk1EP3/TnrvpX1r3e35gJ+1dW31PT2u6v8VOeilDoRGIR6CpVe99L9mampqC18GXfMSPCFQlwL1TFVOqO6lBuGzZMlu7di3zJFKV9/tiGhbXo0cPO3bsWGbzJCoJzp8/P/h65syZlXbjOwQuEeDvw0s4nP6F9oTT4bFofOiZcDtelA6BugXUIJw1a5YtWLCARKJuxeIdqCf+GhaiHoCsJlx3pK6X2anXhBfadSTF96UCGq6nuT9M5C9V4WcEGhegZ6JxQ87wW4FopgpMtgIPPfSQjR071rRGPxsC1Qpoxa8DBw4ESWi1x2Sxn94foGU/X3vtNWNRgSwi4Oc1lSyPHDnSli9fbgMHDvSzEgUoNe0Jt4McjQ89E27Hi9IhUJdAS0tLcByJRF18hT1IDXRNcn7yySedN9ATZq009cwzzzhfVgrojoDmTyiRePjhhxNYLtadelISBNIUoGciTe2cXyuaqea8us5Wz/Xx7s7CFbxgemJ733332SOPPOLE6k3VhMPHMldTL/ZJXoB5N8kbN3IF2hON6CV/bDQ+9Ewkb84VEEhVQOPdX375ZWfHu6eKwcWqFli3bl0wntyFZWCrLbSeMmtOkOYGnT59utrD2A+BYJWy9evX2759+9BAAIEGBUgmGgTkcARcEghf6MXwJpei4n5ZfBreFNVkuFNUhN+rEQiHO82ePZvhTtWAsQ8CFQRIJirg8BUCPgnoyaye0E6fPt2nYlNWBwQWLlwYvOXa14nMEydONCVEPGV24GbyqAiagK1kVL1ybAggUL8AyUT9dhyJgFMCzz//fDAhVf84siFQrUDYm+XT8KZo3fSUWU+YecocleH3jgS02IAWHdBcMzYEEKhPgGSiPjeOQsApAT2V1fhfPaFlQ6BaAU1gzktvVviUeePGjdVWn/0QCJYVVkKxePFiNBBAoE4BVnOqE47D2gpEZ/e33YNPkhIYP368V6vwJOXAeWsT0BNZbVpiNQ+bhvpdddVV9sknn/DuiTwENKU6hKuCaYjosGHDUroql6kkQHuikk7230XjQ89E9jGhBAg0JKBhKtdcc403y3k2VFkOjk1Awzr0grpJkybFds6sT6Q5Hy+++KJpyB8bAtUKhMPkNHdIiQUbAgjUJkAyUZsXeyPglECehqk4BVuAwmhYh4Z3+DrpulyINNRPQ/409I8NgWoFGCZXrRT7IdBWgGSirQmfIOCNgMaHjxo1KliRxJtCU9DMBdTQ3rZtm40dOzbzssRdAD1lVpK0cuXKuE/N+XIuMHXq1OCN6vRO5DzQVC92AZKJ2Ek5IQLpCOgfvGeeecb0DyAbArUIqKE9d+5cU8M7j5uSJCVM9E7kMbrJ1Ukr4enhDJP4kzPmzPkUIJnIZ1ypVQEE9A/elClT6JUoQKzjrKLexaBGts9LwXbkoSRJk2k1Bp4NgVoE1KulhzT0TtSixr5FFyCZKPodQP29FAh7JfI0edbLQHhYaL2LoQgvNtSqPKdOneJFdh7eo1kWWXOI9JCG3okso8C1fRMgmfAtYpQXAbPgHzr9g5e3ybMEN1mBcNhPUZa/VNL00ksvJYvK2XMnoIc09E7kLqxUKEEBkokEcTk1AkkIhL0SercEGwK1CGiuRBF6JUITJU3MnQg1+LNaAT2k0d+v9E5UK8Z+RRcgmSj6HUD9vRPQP3CaJNi9e3fvyk6BsxNQo1orOBWlVyKUfuSRR1jZKcTgz6oF7r33XnonqtZix6ILkEwU/Q6g/t4J6EVjrODkXdgyL/BPfvKTYMnUzAuScgFGjBgRJFF6SR8bAtUKhCs77d27t9pD2A+BwgqQTBQ29FTcR4GdO3cGb7vWP3RsCFQrcPr0aXvqqady+V6Jjgy0stO0adOCF9l1tC/fI1AqoLkTrAhWKsLPCLQvQDLRvgufIuCkwKpVq+yBBx5wsmwUyl2BV155xZYsWZLb90p0JH/33Xfbo48+ynKfHUHx/SUCeiu2Ni2nzIYAAuUFSCbK2/ANAk4JaJjG/v37Czfm3akgeFgYTdhfunRpMKHUw+LHUmRNqJ03bx4TamPRLNZJNOfm1VdfLValqS0CNQqQTNQIxu4IZCWwfv36YLhGVtfnun4KaMw3E/bNNKFW843YEKhFQHNuNERQQwXZEECgfQGSifZd+BQBpwT0dFkNIQ3XYEOgFgENjRs3blwth+Ry33CeEUNWchnexCqlOTcaIqiV0NgQQKB9AZKJ9l34FAGnBMKny7ykzqmwOF8YPU3V0LhBgwY5X9Y0CqgXPe7YsSONS3GNHAk0NzfTq5WjeFKV+AVIJuI35YwIxC7A0+XYSQtxQk28VgNaT1fZLBjuxURs7oRaBejVqlWM/YsmQDJRtIhTX+8EeLrsXcicKXBLS0uhJ15HAxFOxObdAVEZfu9IgF6tjoT4vsgCJBNFjj5190Jgz549PF32IlJuFTKcG8Cb0i+Ny8iRI23Dhg2XfshvCHQgoEUMmMDfARJfF1aAZKKwoafivgisW7fOhg8f7ktxKacjApobMGHCBEdK404xNH9ELyJjdR53YuJDSdSrNWDAAN454UOwKGPqAiQTqZNzQQSqFwiHOIUvT6r+SPYsuoCeot5xxx1FZ2hTf80f0Tsn1OPHhkAtAhMnTmQCfy1g7FsYAZKJwoSaivooEA5x8rHslDk7gcOHD1u3bt2MIU7tx0BDnUgm2rfh0/ICgwcPZqhTeR6+KbAAyUSBg0/V3RdgiJP7MXKxhLt27WKIU4XAaKiTXkSm97ewIVCtAEOdqpViv6IJkEwULeLU1xsBDXFauXKl9e3b15syU1A3BLSK09ChQ90ojIOl0FCn6dOnG6s6ORgcx4ukN2K//fbbjpeS4iGQrgDJRLreXA2BqgUOHjwYjO3mHQFVk7GjWTCx+MSJExaujQ9K+wKjR4+2t956q/0v+RSBMgKah6RknQ0BBL4UIOyAcfcAACAASURBVJn40oKfEHBKQA0djdFlQ6AWAc0FGD9+fC2HFHLfW265hfHvhYx8Y5XWPCQl66wG1pgjR+dLgGQiX/GkNjkS0Go8avCwIVCLgJIJTTBmqyygRqEmqR8/frzyjnyLQERAyToT+CMo/FpoAZKJQoefyrsqoAYOq/G4Gh23y7V+/Xq7+eab3S6kI6XTUKdf/vKXjpSGYvgiwGpgvkSKcqYlQDKRljTXQaAGATVw1NBhQ6AWgTAJ1aozbB0L3HbbbTxh7piJPSICStaVtLMhgMAXAiQT3AkIOCigLnQm0DoYGMeLRBJaW4BoFNbmxd5fCITJOkPkuCMQ+EKAZII7AQEHBfTUi/kSDgbG8SKRhNYWIBqFtXmx95cCmjfBELkvPfip2AIkE8WOP7V3UCBcJYS3FzsYHMeLtHv3bpLQGmOkRuHRo0drPIrdiy6glfb0pnk2BBAwI5ngLkDAMYEPPvjARo0a5VipKI7rAkpCN2zYYCShtUWqX79+vG+iNjL2NrNevXrZ/v37sUAAASOZ4CZAwDmB9957j7cXOxcV9wukJFRvdWarTaB///40CmsjY2+zYE7bypUrsUAAAZIJ7gEE3BPYtWuX9e7d272CUSKnBZSEqmHMVptAjx49jEZhbWbs/YXA1KlTGerEzYAAyQT3AALuCWzbts169uzpXsEokdMC77zzjt14441Ol9HFwnXq1MnGjRvHy+tcDI7jZRowYIAdOXLE8VJSPASSF2DORPLGXAGBqgU+++wze+ONNyxcZabqA9mx8ALvv/++XXPNNYV3qAdAyzB//PHH9RzKMQUW0ItFP/zwwwILUHUEvhAgmeBOQMAhgWPHjjHu3aF4+FQUDdXh3ST1RWzo0KGmYWJsCNQioGGFBw4cqOUQ9kUglwIkE7kMK5XyVUBd5gxx8jV62ZVbL8/SUB22+gSuvfZa0zAxNgRqEbj66qtNw1LZECi6AMlE0e8A6u+UwLlz50xd52wI1CJw/vx5eiVqAYvsq+FhZ86ciXzKrwhUFtBwVA1LZUOg6AIkE0W/A6i/UwKs5ORUOLwpjIZasJJT/eHSik4LFy6s/wQcWVgBVnQqbOipeIkAyUQJBj8i4IJA586dXSgGZfBM4PLLL/esxO4UVys6sSFQj8CVV15Zz2Ecg0CuBEgmchVOKuO7gJ6O6ikpGwK1CNCjVYtW+/vyhLl9Fz6tLMAk7Mo+fFsMAZKJYsSZWnokwFNSj4LlUFHp0WosGDxhbsyvqEfTI1jUyFPvUgGSiVINfkYgQwFW5MkQ3/NLq0dLK8uw1S+gVdR4AVn9fkU9UskEK4EVNfrUOxQgmQgl+BOBjAVYkSfjAHh+eV502FgAtYqaVlNjQ6AWgV69erESWC1g7JtLAZKJXIaVSiGAAAIIIIAAAgggkLwAyUTyxlwBgaoEeGFdVUzsFBE4fPiwafIwW2MCenGdJrKzIVCLAC+uq0WLffMqQDKR18hSL+8EeGGddyFzpsBMHm48FHpxHRsCtQrw4rpaxdg/jwIkE3mMKnVCAAEEEEAAAQQQQCAFAZKJFJC5BAIIIIAAAggggAACeRS4LI+Vok4IIIAAAukIaM5GuJ06dco++uij8NcO/9SymloNJ9w0/pxVqUIN/kQAAQT8ECCZ8CNOlLIAAidOnLA+ffoUoKZUMU6BAwcOmN7Cm8T22Wef2bFjxyxMErSe/pkzZ2zbtm32xhtvBJfU5O/SORtDhw6tuihKRLZs2XJx/9LzTp8+PfhcdVPSoT/1Yr7u3btf3D/OH/Tmeb2vY8GCBXGelnMVQOD222+306dPkwgXINZUsX0Bkon2XfgUgdQFPvjgA2tubk79ulzQf4E43sKrlyYePXrU3n33XVOCEjbs1ajv0qWL9evXz0aOHGmaqPzYY48l1qhXNMIkRj+rLFqcYOXKlabkY8OGDcHqVQMGDDC9G0JJRhxJOG+e9/+/g6xqMGrUKPv4449JJrIKANfNXIBkIvMQUAAEEEAgfQE1zNVQ13KoShy0jR8/PkgaJk2aZE8++WRmjSM17MMEIfwzFAoTDS2lrDps3LgxSDTUQzJixAi78cYb7eabb86s7GE5+RMBBBAoigDJRFEiTT0RQKDQAup5+OUvfxkMK9JwnrDxPW7cuEwTh1qDEiYaSjLCnrwVK1YEiYWSI/VcDB8+3FSvCRMm2K233mp9+/Y1eh5qlWZ/BBBAoDoBkonqnNgLAQQQ8E5g3759tmPHjiCB0JycKVOmBI3sOXPm5K5xreRC/1MCoXkPYc/LD37wg6DnYt68eTZ48ODgf0zy9u5WpsAIIOCwAMmEw8GhaAgggECtAmECsXr16mBOgRrXS5cuTXSOQ61lTGP/0uRi8eLFtnfvXnv99ddtzJgxQa/MxIkTSSzSCATXQACB3As0tba2tpbWsqmpySIflX7NzwiUFeDeKUtT1Rdq8JUO3ajqIHYqvEBLS4tp8r6etuse0qRk9UBoUihP4NveHppzESYWTz31lKnHQhPLBw0aFKwWxb9/bc34pLKA/u375JNP+O+tMlNN39KeqIkr9Z2j8SGZSD0E+b1g9ObKb02TqZkahdr0JJkNgY4EwkbxX/3VX9n27dtNDWNNoE5q6dSOyuPj96HhqlWr7Oc//7lde+219uMf/5hGoY/BzLDM/NsXPz6m8ZvGecZofEgm4tQt+LmiN1fBOWquPslEzWSFPEDr2b/00kumYUzqfdATdT1p5/0Ijd0Of/d3f2ff//737Te/+U3gqgncw4YNa+ykHF0IAf7tiz/MmMZvGucZo/H5Spwn51wIIIAAAskIaELx/Pnz7c477wwu8NprrwUJhJIJtsYFrrvuOrvtttuCeRVKJLTilXp6Nm/eHLz3ovErcAYEEEAgnwIkE/mMK7VCAIGcCCiJmDFjhk2ePDl4B4QmEU+bNo2hOAnFV0vIqkdi/fr1QbKmN3RrToV6DjUsig0BBBBA4FIBkolLPfgNgcwE9BZjLd/JhoAEwiRCiYSelO/evTuYT9Pe+xK0L1tjAqdOnWpzAi2IoOFja9asCV7uR1LRhqjwH2jY4e233154BwCKLUAyUez4U3uHBHr16hWsyuNQkShKBgLRJEJPyCuN3VeDVy9qY2tM4KOPPrKhQ4e2exKSinZZ+NDMPv7442CODRgIFFmAZKLI0afuCCDgjIDeUB0OZxo9enQwzKZSEuFMwQtUkPaSip07dxZIgKoigAACbQVIJtqa8AkCmQh07tw5GNqSycW5aGYCGoev90P06NEjeDKuORHNzc01lUfDLDTcgq1+AQ0x1FDDarbSpCKcqM1Qs2rk8rfPkSNHrEuXLvmrGDVCoAYBkokasNgVgSQF9H4AhqskKezeubVSkMbhnz17Nnjpld4x0t6ciI5KriViNdyCrX4BvfhPQw1r2ZRUaBjaI488EkyQ12pbJHW1CPq/77lz54KFEfyvCTVAoH4Bkon67TgSgUQEWDEmEVanTqohTQ899JAtW7YsmNw7c+bMhldnOn/+vFN19K0wn376ad1FVk+SepT0QEBL94bvjKn7hBzojYCSCTYEii5AMlH0O4D6OyUwffp0O3bsmFNlojDxCShR1Mvm1AMxduzY4Km2nm43umni8HvvvdfoaQp9/MqVK62RWKhHacqUKUFyuHHjxiBZVNLIlm+BAwcOWP/+/fNdSWqHQAcCJBMdAPE1AmkL8IQ5bfF0rqcx9ffdd5+p8aEXzimhiHPjCWn9mnH2BiohWbFiRZAsah4MvRT1x8WHIxvp0fKhfpQRgWoESCaqUWIfBFIS4AlzStApX0YNSr10TmPr9d6Crl27xloCPRlVksJWn4B6A9UrGOemZFHnpZciTlX3ztVoj5Z7NaJECNQucFnth3AEAggkJaDVZFgVJind9M+rYS5z5swJLqzeiLiTiLBGrAQWStT3p15Yl8SKPJpDoV4KJZPqpdi0aVPNK3XVVyOOSkOAF9alocw1fBCgZ8KHKFHGwgjw4rr8hFrvHwjnRqhBmVQiITFWAmvsvtEL6/r169fYSSocHfZSaMK9VnyKc1hVhcvyVcICvLAuYWBO740AyYQ3oaKgRRDQ00utW8/mr4AainpvxOOPPx5Mxo17bkQ5malTp9KrVQ6ng8937dplvXv37mCvxr5Wwrd27drgJJo7w+TsxjxdOJrJ1y5EgTK4IEAy4UIUKAMCvxXQijC8gMzf20ENxMcee8z0zgItFdrI6kC1Ktxwww2m4TpstQtoaOHVV19d+4E1HqH/vrUMsObO6MEBb8+uEdCx3fWiw+uuu86xUlEcBNIXIJlI35wrIlBRQC8gU2OUzS8BNUjVCzFixIhgknU9L59rpMYapvPuu+82copCHqueJL0sUj0HaW16L4UmZ6v3Sr1YbH4K7N+/v+YXHfpZU0qNQGUBkonKPnyLQOoCrOiUOnnDF9SbrLVa06JFi4J3DTR8wjpOwIpOdaCZBY36uFdyqqYkSl7Ue6UGqV5gyDyKatTc2oeVnNyKB6XJToBkIjt7roxAuwIau60x3Gx+COjJ8qxZs4IVe4YNG5ZZoTVMh/k2tfNnOe5dvVeanD9gwIDgHSTMo6g9flkdoZ5IzVNiQwABM5IJ7gIEHBPo2bOnbdu2zbFSUZyogJ4kz5gxI3iyrCfMaQ6TiZZFv2u1qHHjxjGxtz2cCp+98847duONN1bYI/mvpk2bFsyj0DA5loZO3juOKxw5ciRIAuM4F+dAwHcBkgnfI0j5cyegRmG3bt1oFDocWSUSmmitdxMsXrzY0p4fUY5myJAh9stf/rLc13zejsD69evt61//ejvfpPuR5lFomFzfvn2ZmJ0ufV1X27Nnj9122211HctBCORNgGQibxGlPrkQoFHobhjDFZs0NEUr87iSSEhs8ODBPNmu4dbRS8e0Zd2rFBZZw+TCidms9BSquPmnK0momzqUqmgCJBNFizj19UKARqGbYVIioaEoSiQ0NMW17ZZbbrEtW7a4Vixny3Pw4EEbP368U+VTYqM3ZmulJ03sZ3NPwLUk1D0hSlQ0AZKJokWc+nohQKPQvTCFicTcuXOdTCQkpoao1r4PGzvuKbpVorfeeivozXGrVF/EUQmFJvazdKxr0THTECfXklD3lChRkQRIJooUberqjUDYKGR1FzdCFiYSGtOuse0ub2rk6Ik7W8cC6sVR4u7iFvZQrF69moTCsQApmVDvMRsCCHwhQDLBnYCAowJTpkxhMq0DsSlNJLJc+rVaCjVytLoUW2UBxVW9OGq0u7qRULgZGc2XIJlwMzaUKhsBkols3LkqAh0KaKUQPQFjy07At0RCUmrkqLGT3XbMWu6/yZqamqyp6W577s0zZhdO2u5F91u3pia76bk37fPsCnfxylr1Sgm761tpQsEciuyjpb8TtNqeVt1jQwCBLwRIJrgTEHBUYNCgQfbUU0/xZtyM4qPlXzXZWhOtfeiRCJnCpYWze19BD5vw4q/sn4+/bN+5/m/tL/56k/30r5bbgbFL7ERrq/3qz79hl4WFzfBPDXHyZWnPMKHQHApWecrwpjGzrVu3Bn8vZFsKro6AWwIkE27Fg9IgcFFAS47qDauHDh26+Bk/pCMQvkdCT659eHodVVESlPVb1L/yu//G/u2ffsNOLphr/9fXH7AH+l0RLWZmvyu+elu4EnZftjCh0CpPJBTZRW379u126623ZlcAroyAgwIkEw4GhSIhEApMnDjRduzYEf7KnykIhImEq8u/VkNwxx13BMuLVrNvcvt0tcFjmu16u9mG9b/WXPrHZu/evTZv3jyn3hFSTRyUUKxZs8aGDx/O+0SqAYt5H62Stn//fhs4cGDMZ+Z0CPgt4NLf735LUnoEEhDQ+Het5sKWnsALL7wQXMzF90hUq6BGpyYXa3x3dtvn9g9nzprZDvvxjiN2IbuCtLmyJqj7OoG2T58+wQOGyZMnZxzfNqy5/0Bz2Hzsqcx9YKhg5gIkE5mHgAIgUF5A49/1hHzfvn3ld+Kb2ASUuOnJ4+LFi2M7Z1YnUqNH47uz2i78+hX7/t/+S7tvlNkvDp2wc1kVJHJd9TxpLpKvyYSqozk84ftOVB+2dATWrVsX9AqlczWugoA/AiQT/sSKkhZUgKFO6QRe49D1grCnn37au+Ev7QnpfRh68Vkm24Wjtv77P7fm//y0/fs/HW4nf7TF9vx6ly2aucF+nXEXhYY4TZ8+3fvVeBTf0aNH22OPPZZJiIt2UYY4FS3i1LcWAZKJWrTYF4EMBMKhTjyBTA5fw4E0Dl3j0TVEKA+bhsNoS3VVp8/ftOduarKmP/ovZn/2lE343cut24A/sFEnV9n3F5+wb8/8Y/vdjP/V2bBhg40bNy4PIb74Jnbekp18OLdt28YQp+SZuYKnAk2tra2tpWXX2uCRj0q/5mcEygpw75SlafiLhx56yB544AGvlihtuNIpnUBJ2siRI01vt/ZpCdhqeDRs6+zZsxcbndUck+d99HT5qquusvPnz+ei90mxyvP969K9qDfLz549m8nXKQWF9kRK0HVeJhqfjJ8R1VkLDkOgYAJKJPRElS1+AQ1r0vyCvCUSkrr77ruDCfz0an1x3+jp8pIlS3KTSKhWWkJaw9nUs5bthPv4/9t05Yxh7x6rOLkSEcrhmgDJhGsRoTwItCOg9fDVENKTVbb4BNQI+/TTT+3BBx+M76QOnSmcwK95AmwWJFZqdOdt09C8TZs2BT1QJI7xR1dvHmcVp/hdOWN+BEgm8hNLapJjAT191D9mr7zySo5rmW7V9LTxmWeeyc2E63J69Gp9IROuiJbXp8uakD1kyJBguF65e4HPaxdQcvboo4/aqFGjaj+YIxAoiADJREECTTX9F9CYXSZaxhNHNRC0Tr/mSeRlwnU5mbBXq+hDYF599dXcP13W27F3795tepLOFo+A3nitFxyql48NAQTaFyCZaN+FTxFwTkCNXr1zQkuYsjUmoCRCyVke50lEZdSrpRfwrV+/PvpVYX7X8EC9W2Ls2LG5rrNirQcOs2bNYv5ETJFetmyZ3XXXXTGdjdMgkE8Bkol8xpVa5VRAQ1ZWrVqV09qlUy09tdXTWz3FLcqmidgaqlHU8fQaHpi3idfl7l09dHjyySdtzpw55Xbh8yoF8j40rkoGdkOgQwGSiQ6J2AEBdwT0JP3UqVPpvjvAneo3XBI9odZT2wULFuRqRZ+OYDREQ0M1Nm7c2NGuufteCZSe1qsnqijbhAkTgqpm9tLCnEC/9NJLwQsOc1IdqoFAYgIkE4nRcmIEkhHQROyVK1cmc/Kcn1UTrjXkJ3yhW86re0n17r333mDCedF6J5RAafJs3ufGXBJss2BhgXvuuYfhTlGYKn/XAg1aQU9zjtgQQKCyAMlEZR++RcA5AY371j9yRZ9QW2tgNNdEDYSJEyfWemgu9lcCpUZ10ZaJ1Yv7pk6dmosY1lIJJU8vv/wyw51qQSvZ9yc/+UkwXEzzUNgQQKCyAMlEZR++RcA5Af3jpjHRRZ5QW2tQ9DRecySKNrwp6qRG9cKFC6Mf5/Z3JZBKoorYE6WghsOdWN2ptltcwyH192veJ+zXpsLeCJQXIJkob8M3CDgroH/k9MSVl9hVF6IXXnghGDNf1EZlqBQ2rIuyIpgSpyL2SoTx1p/Tp08P5gnxd0WpSuWfNVdCD2zolajsxLcIhAIkE6EEfyLgkUDYO6F/9NgqC2hokxKvIq3eVEmkKL0TRe+VCO8BJZCaZ/X888+HH/FnBQElXfr7gl6JCkh8hUBEgGQiAsKvCPgiEPZOqLHMVl5AT6fnzp3LU8bfEoW9E3ke+qJhbfRKfPnfxIMPPhgM2+Hvii9Nyv2kRRrolSinw+cItC9AMtG+C58i4LxA2DvByk7lQ6Wn01pKt7m5ufxOBfxGvRNaIjevKztpBacwaSpgeNtUWX9XKKEu0nyZNghVfKBkS4tb0CtRBRa7IFAiQDJRgsGPCPgmoH/09I8fTxzbRq500nXbb4v9iRraWtkpj++dUNz1dLnocyWid7gSaiXWRZkvE61/Nb/rwQy9EtVIsQ8ClwqQTFzqwW8IeCWgJ46LFi2yGTNmeFXuNAobvl9ADWe2tgKPPfZY0OjO28TcdevWMdm+bbiDT7SameYO5bVHqky1q/pYSZYeyoQrYFV1EDshgEAgQDLBjYCA5wJ6K7a2PI+BrzVE4dNpNZjZ2hfQewg0MTdPk/iVGN1///323e9+t/1KF/zTPPdINRJa/X2hIWBa+YoNAQRqFyCZqN2MIxBwTkBPHPM8Br5WcC0Fq4Zy0d56XKuTJuZq5Zq8DJPT8Ca9qK1r1661UhRmfw3/khO9E1+GPJxjEz6Y+fIbfkIAgWoEmlpbW1tLd2xqarLIR6Vf8zMCZQW4d8rSpPLF/Pnzg8azGtFF3vR0+qqrrrJPPvmERmUVN4J6tDQ0aMWKFVXs7e4u+/bts9mzZ9vatWtZuauDMGlY5NChQxnSYxa8q0d/Xxw7doyHDx3cN2l+TXsiTe3arxWNDz0TtRtyBAJOCmhox9KlS3PzlLleZA3bWbJkCYlElYDhSlctLS1VHuHebnrK/vDDDwfJhOYRsVUWoHfiSx/10rz44oskEl+S8BMCNQuQTNRMxgEIuCmgoR1FX/5RvRKPPvqoTZo0yc0gOVoqjRVXo8rXydjqWdHqVAMHDnRU2K1iMXfii3ioN0tD/CZOnOhWgCgNAp4JkEx4FjCKi0AlgTw8Za5Uv46+0zK59Ep0pNT2ezUup02bFiQUbb91+xM1BtUjpyU92aoXKHrvBL1Z1d8r7IlARwIkEx0J8T0Cngk8/fTTds8999jx48c9K3ljxVXjQE/Xx48f39iJCnq0ns6qYe7TqmCKucb/q0eOSde13bhh78TevXtrOzAne2tJbf1dQW9WTgJKNTIVIJnIlJ+LIxC/gFYw0oo2c+bMif/kDp9x+/btwVAXVnCqL0iaaxCuCubLcCcNb1KjOOyRq6/mxT1KwwGL+FZsDW9av3598M6N4kafmiMQnwDJRHyWnAkBZwTCFy/5PKm2Vsxly5bx1uNa0SL7+zTcieFNkeDV8Wv4VF6N66Js4fCm5cuXs+pXUYJOPRMXIJlInJgLIJCNgIY7adiPGl1538LGkBrDbI0JaLjTp59+ai4nomoQTp48OXj7O8ObGou3Jt/n6cWFHWno70Utnx0mUh3tz/cIINCxAMlEx0bsgYCXAhruo7HkGlOuxleeNzWGHnnkkTxXMbW6abiT6/NuwvHuvGSs8dti0KBBpoULfBna1kiNNR9ID1f0skY2BBCIT4CX1sVnWfgzRV9iUngQRwD0MjttM2fOdKRE8RZDjSC9dOr8+fMMW4iRVg0vDR1z7SVwrpYrRvrUT6XVsK644orgiX3qF0/pglqQokePHrycLiXvRi9De6JRwWSPj8aHnolkvTk7ApkLPP7447Z7926vVumpBe2VV14JloPlZWW1qHW8ryY1DxkyJBhK1PHe6eyhBuGYMWOCpWCJd3zmWtVICUVeN/XMaunjTZs28XK6vAaZemUqQDKRKT8XRyB5ATW61FCYNWtWLudPaGw/q/kkcx+FiagL8yfUINTCAjQI44+1hkQOGDDAdu7cGf/JHTijhu2NHj2avycciAVFyKcAyUQ+40qtELhEQI0FjTPXpNU8jY1m4vUlYY79lzARdWEifzhxlsQx9jAHJ9TE+9dffz2Zk2d41tWrVwcLCjBPIsMgcOncCzBnIvchTq+C0TF06V2ZK1UroB6K/fv32+LFi3Mxv0D16datW/DEuloD9qtdQE+s1UuhHoos3uORt/u29ggkf4R6fjp37pyruUdZ37fJRy2/V6A94XZso/EhmXA7Xl6VLnpzeVX4AhVWqzv17NkzGEPse7U1pv+1117j7ccpBFKJxMaNG1NPRMMGoZ6aM08i2UBrsYaRI0daHlbJ0vwaDYtbs2ZN8GLDZOU4e9wCtCfiFo33fNH4MMwpXl/OhoDzAnoztnon1P3v86YhThrnzXsG0omiGmbyfuyxx9K5oJkpxmGPCIlE8uxKJFatWpX8hRK+goZy6n7V0E7ePZMwNqdHwMxIJrgNECiYgBplGn+uoSM+T7jcsWOHaZw3W3oC4bhz3TtJb3qy/PDDDwcNwiyGViVdPxfPr3dOrFy50uv30mi41hNPPBEsc5uHHhYX7xPKhEBUgGQiKsLvCBRAQI0zDVvRU19fEwr1rAwePLgA0XKnikpENd9GPVtJJhThEBU9WaZBmF78Fd958+bZ3r1707tojFdSIqGeM/WgaSlYNgQQSEeAZCIdZ66CgHMCSiiWL19uw4cPNzXefNoY4pRdtMKeLSVzSSSiahBqKN6UKVNIJDIIs4Y6+bqqk5JPbSQSGdw4XLLQAiQThQ4/lS+6wMCBA03DhTS+2KeE4u2337YRI0YUPXyZ1T+pni2eLGcW0osXvvnmm+2pp566+LsvP6in7P333w96znwpM+VEIC8CJBN5iST1QKBOAQ0j0RM9nxIKDdEaOnRonTXmsDgE4k4oSCTiiErj59CCBlOnTg0mvzd+tnTOoEQiT0tep6PGVRCIT4BkIj5LzoSAtwI+JRRaqeXEiROs0uLA3RZXQkEi4UAwS4qgXj/1/vmwkUj4ECXKmHcBkom8R5j6IVClgC8JxcGDB238+PFV1ordkhZoNKEgkUg6QrWfX71+27dvr/3AlI8gkUgZnMshUEaAZKIMDB8jUEQBHxIKTQ5lFSe37s56EwoSCbfiGJZG72ZwfYlYEokwWvyJQPYCJBPZx4ASIOCUQGlCcfjwYafKpsKsX7/ebrnlFufKVfQC1ZpQkEi4fcdMnz7dDh065Fwhdd+QSDgXFgpUcAGSiYLfAFQfgfYEwoSib9++iSz/2d41q/lM8yW0qeHK5p5AaUKhBl+5TSuHaQlS3gdQTij7zzXUEgWEfgAAIABJREFUybV5E2ECymTr7O8PSoBAqQDJRKkGPyOAwEUBJRR6MqkX223evPni51n+wHyJLPWru7YSitdee63si+3CF9LNnTuX9wFUR5rJXv3793dq3oQeJIQvpNOLE/W+EzYEEHBDoKm1tbW1tChNTU0W+aj0a35GoKwA905ZGq+/CBt/eolY1i+D0ovSLr/88mAZW69RC1D48Cmyqho2/vSSO70kUe82UbLK5q6A4te5c2cn2gMu/R3kbsTyVTLaE27HMxofeibcjhelQyBzAT1p1qRnDS2YMWOGqZGR1aYVZvTElM19AT05VhKhoUz33Xef/eVf/mXQy6XeLhIJP+Kn901kPW9KCajegaN34WT9MMP9qFFCBLIRIJnIxp2rIuCVQNgw7NKlSzDUQE8Ks9i0wkyPHj2yuDTXrENA982DDz5oX/va12z+/Pn2/e9/n/eD1OGY1SFKBI8cOZLV5U0vp9Qwy+XLl5OAZhYFLoxAxwIkEx0bsQcCCJgFY5RnzpxpY8eODZ4U7tu3L1UXJTDjxo1jrHSq6o1dTDHTOPff//3ft7/5m7+x733ve0EDsbGzcnRaAloiNoueCfV+KvncuHFjcL8MHDgwrSpzHQQQqEOAZKIONA5BoMgCGnKgJ4UPP/ywaQ5DWtvRo0dtyJAhaV2O6zQoEA5PUfKpJPSb3/xm0DBUAzHr4XINVq0wh/fq1cs++OCDVOurBFTD4rRpmBwrt6XKz8UQqEuACdh1sXFQewLRCTnt7cNn+RHQ6ipPPPFEUKFnn33WunbtmmjlNORBm5IZNncF9FT5hRdeCBLNNWvWtBnW1NH37taseCVTrNKchK1V48aMGWObNm2y5ubm4oFT44sCtCcuUjj5QzQ+9Ew4GSYKhYD7AkoeVqxYYSNGjLA777zTkh72tGvXLuvdu7f7MAUuYTisSU+zNWlfw2Sim+ZRaCKtJtROnjyZYU9RIId+V6xuv/12C9/vklTRwmFNy5Yts2PHjpFIJAXNeRFISIBkIiFYTotAUQS0ZGw47EnjnNUwSGLT2G09JWVzU0BPlTU5XsOaFixY0OHcFq3opN4mDXt66KGHEm+wuqnmfqlGjRplH3/8cWIF1UMIvcBQ29q1axnWlJg0J0YgOQGSieRsOTMChRHQBEk9idam8c5JTNrcsGFDu0+6C4PsaEX11FpzINatWxc8Va5lGJrGw6t3SwmIerdceTmio9SZFKtnz5524MCB2K+thw6ac6W5V3oYoXk16glhQwAB/wRIJvyLGSVGwEkBNQTUIJg9e3YwfGXp0qWx9VKowarhFmxuCahnQUmA3v3RyGRZJSCaX6FhLkpMNFyKzQ2Bbt26xV4Q9UbooYPirIcQrNYUOzEnRCBVAZKJVLm5GAL5Fwh7Kc6ePRsMX9CqPo1uGmah4RZsbgioEaihSeHSnRrq1uhTZc2vWL9+vQ0dOjQYLhVOuHejxsUtheYpab5SHJseCmgopHoj9NCB3og4VDkHAtkLkExkHwNKgEDuBMJeCg1fWLhwYcNPm0+dOmV6YR5btgLh0BT1JGhokoYoxb10p86tSbhqwI4fPz6RIXPZKvp19bjmKYW9WFdccQW9EX7dApQWgQ4FSCY6JGIHBBCoV0C9FJpUGT5t1hjpeiZof/TRR9avX796i8FxMQhoPoMmyqpX4rXXXkt0iV4lKJrEPX369GDInIY+Jb2iUAxEuTzF1Vdfbdu2bau7bpo/paRQvVgayqaVvBrtxaq7MByIAAKJCJBMJMLKSRFAIBRQw0FPmz/55JOgIaoGKUNYQh33/wwbg5pgrcaghqYk/U6RUEUrPmlMvZLRq666KpiwW08yGp6PP2sXUKzfeOONmg9U0qkkUMv/KilUL1Z7SwXXfGIOQAAB5wRIJpwLCQVCIJ8CapSoIaoGaTiEpdr5FLxjIv17QkmEGoP6X5aNwdJkNJyHo2SUpCLde6Jab/UgafEFPUBQEqhkUEkhGwII5FeAZCK/saVmCDgpoKeT4RAWzafQEIhqkoq4xm47ieJQocIkQk+U1RjUMDUXGoNKRjVEJkxGwx6uahu5DhF7VxQlk5rHUmkLkwj1IGkLh8IxpKmSGt8hkA8Bkol8xJFaIOCdgBqoWr1HDZVakgrvKupJgaNJhJ4o6+mya43BMBklqXDjxoomERrOqKQvraFwbihQCgSKLdDU2traWkrQ1NRkkY9Kv+ZnBMoKcO+UpeGLKgTUO7Fq1SrTyk1aalSrBYUN2SFDhgRPOmmgVAFZ4y6V3Gs8VSa7Kwn6yU9+EiSmum8mTZpEQzbmSGio29SpUy+Z84B7zMic7hIB2hOXcDj3SzQ+JBPOhcjfAkVvLn9rQsmzFFAjZeXKlcEKMmHjUEMneMgRX1Q0NEir62h1LW3qHXJhKFMjNdQT8pdeeskeffRRmzdvnt17772XNH4bOXfRj1UyoSRNq7OFyef+/fvtySefvCTpL7oT9Y9PgPZEfJZJnCkaH5KJJJQLes7ozVVQBqodk0DYOFSDV6vJ7NixwwYNGnSxtyKmyxTqNErUtMRrnhvc0UTpkUcesREjRnDfNHCnayWmX/ziF8HCCQMGDLAHHnjA++SzAQ4OTUGA9kQKyA1cIhofkokGMDn0UoHozXXpt/yGQH0Cahxq8rWGWehpqHormpubeepcJaeSsldeeeXicrzy09vEizBkbN++ffbqq6/aU089FfRW3HXXXcHT9SrpCr2b/rvbvn27aUlgvWdC98zTTz8d+0sKC41M5csK0J4oS+PEF9H4kEw4EZZ8FCJ6c+WjVtTCBYHw3oo2jDVB+I477qCBEwmSnPbs2RM0BEnALFhGNmwYhx7Dhw8nsYjcN0og9u7dGyznGiZgWjVLL43Upv/e2BBIQyD8Oz+Na3GN2gWi8SGZqN2QI8oIRG+uMrvxMQI1C7R3b+mlWFu3br34xF0NnVtvvbWwDUR57N69O5gLQYO5/C3WXqJ12223FXYIXeixZcuWYFU1zTdRAlE6pDB8ySTJRPn7im/iFWjv7/x4r8DZGhGIxodkohFNjr1EIHpzXfIlvyDQgEBH91aYWOjpsyZvq0E0ePBgu+WWW3Lba6FG4MGDB+2tt94KJlJ369bNRo8ebTxxr/5GizakNZROq4j1798/t8Po1Ptw6NAhe/vtt4NE/MSJE8G7XqIJRKkiyUSpBj+nIdDR3/lplIFrlBeIxodkorwV39QoEL25ajyc3REoK1DLvVXayNbT1rCx1K9fP68biUqYjh49GiQPqteGDRsKkTSVvSli/qK0kR0mpVrlSi/u6927t/Xt29fLSdzhfw/vvvtuMAdCyXZYr2qTJpKJmG82TtehQC1/53d4MnaIXSAaH5KJ2ImLe8LozVVcCWoet0Aj91bYmNITfA3/UWNKT6C1Ko2e5qtBdfXVVzszIVmNWr1t+MiRI/bhhx/agQMHguEn48aNM71vI+89LnHfO/WerzS5iMZAiakSDN033bt3r/cSsR+n1br0nhbNcdi1a1cwcVoX0eRpJUXVJg/RgpFMREX4PWmBRv7OT7psnN8sGh+SCe6K2ASiN1dsJ+ZEhReI+95So6u0sa7VarT8rJ7YalPDS5saX9riTDbCZEHnVRnOnTtn77zzjp05cyZo/IXl6NKli4W9KT169PDyqXiAl6P/C3uH9JRfCUZ43yg5vfLKK4P75fLLLw8SDa1Apv/FmWzovtUWJgzqdfvggw9Mn6unSuW44YYbgvtGyU7Pnj1jSZJJJnJ0E3tSlbj/zvek2t4UMxofkglvQud+QaM3l/slpoS+CKRxb4WN/LChpka+GozawkZj6BU2HsPfO/pz4cKFl+wSJi1q7Kl3RA3QXr16xZq0XHJBfklUQI358+fP23vvvRdcR70C2sJGfnhx9S716dMn/LXDP8vdd2GiqRMo4Y07aYkWjGQiKsLvSQuk8Xd+0nXI8/mj8SGZyHO0U65b9OZK+fJcLscCrt1b4RPiasnpWahWKt/7qWdDSUe1W5w9YtVes739SCbaU+GzJAVc+zs/ybr6eO5ofC7zsRKUGQEEEMhSoJany1mWk2u7JRDnkKc0a6Zeuuuuuy7NS3ItBBDwSOArHpWVoiKAAAIIIIBAygIa7qdheGwIIIBAewIkE+2p8BkCCDgloDkKtQ4tcqoCFAYBBBBAAIGcCpBM5DSwVAuBPAlopRw2BBBAAAEEEHBPgGTCvZhQIgQQQAABBJwRUK+gVoxiQwABBNoTIJloT4XPEEDAKQEtoap3MrAhgED6AnqHha+Tx9PX4ooIFE+AZKJ4MafGCHgnoHcxaEUZNgQQQAABBBBwS4Bkwq14UBoEECgjQDJRBoaPEUhQQEOc9LI9NgQQQKCcAMlEORk+RwABZwT0lt/wbdTOFIqCIFAQAd6rUpBAU00E6hQgmagTjsMQQCBdgU8//TTdC3I1BBAI5ippzhIbAgggUE6gqbW1tbX0y+grsku/42cEKglw71TS4btGBbi/GhXkeARqF2hpaQkOmjBhQu0HcwQCdQrw932dcCkdFo0PPRMpwXMZBBBoXOCzzz5r/CScAQEEqhbYtWuXXXvttVXvz44IIFA8AZKJ4sWcGiPgpcD06dPt2LFjXpadQiPgq4CGF15zzTW+Fp9yI4BACgIkEykgcwkEEGhcgHdNNG7IGRCoVWDlypXGBOxa1dgfgWIJkEwUK97UFgFvBfSuiQ8//NDb8lNwBHwTOH78OMvC+hY0yotABgIkExmgc0kEEKhdgOVhazfjCAQaEfj444/plWgEkGMRKIgAqzkVJNBpVDM6uz+Na3KN4gho8nXnzp0tsgBdcQCoKQIpC7CSU8rgXO6iAO2JixRO/hCNDz0TToaJQiGAQFSgU6dOdvvtt5uGXrAhgEDyAlrJqXfv3slfiCsggIDXAiQTXoePwiNQLIHx48fb0aNHi1VpaotARgLbtm0zXliXET6XRcAjAZIJj4JFUREoukC/fv3s3XffLToD9UcgcYGwB7Br166JX4sLIICA3wIkE37Hj9IjUCgBTcLevn17oepMZRHIQkA9gOoJZEMAAQQ6EmACdkdCfF+1QHRCTtUHsiMCNQjoPjt//rxpDgUbAggkI7B06dJgJafm5uZkLsBZEaggQHuiAo4DX0XjQ8+EA0GhCAggUL3A1KlT7dChQ9UfwJ4IIFCzwJYtW6xXr141H8cBCCBQPAGSieLFnBoj4LXAiBEj7O233/a6DhQeAZcFTp8+bSdOnOAdEy4HibIh4JAAyYRDwaAoCCDQscCtt97KvImOmdgDgboFDh48yHyJuvU4EIHiCZBMFC/m1BgBrwUGDhxoK1euND09ZUMAgfgFXn/9dRs8eHD8J+aMCCCQSwGSiVyGlUohkG+BefPmmZ6esiGAQPwC69evJ5mIn5UzIpBbAZKJ3IaWiiGQXwE9NdXTUzYEEIhX4PDhw9atWzfj/RLxunI2BPIsQDKR5+hSNwRyKqBkQk9P2RBAIF6BXbt22YQJE+I9KWdDAIFcC5BM5Dq8VA6BfAroqemAAQNs3759+awgtUIgI4GWlhYbOnRoRlfnsggg4KMAyYSPUaPMCCBgEydOtB07diCBAAIxCRw/fpwlYWOy5DQIFEmAZKJI0aauCORIQEOdVq9enaMaURUEshXYunWrTZkyJdtCcHUEEPBOgGTCu5BRYAQQkABDnbgPEIhXQEOcmpub4z0pZ0MAgdwLkEzkPsRUEIH8CjDUKb+xpWbpCmgVJ219+vRJ98JcDQEEvBdoam1tbS2tRVNTk0U+Kv2anxEoK8C9U5aGLxIS0IvrrrrqKjt//rx16tQpoatwWgTyL7B06VK74oorGOaU/1B7UUPaE26HKRofeibcjhelQwCBCgIa6qQX2G3fvr3CXnyFAAKVBD777LNg/tHdd99daTe+QwABBNoVIJlol4UPEUDAF4GRI0faunXrfCku5UTAOYG9e/faqFGjeFGdc5GhQAj4IUAy4UecKCUCCJQRGDZsmO3fv9+0rCUbAgjULrBq1SobN25c7QdyBAIIIGBmJBPcBggg4L3AtGnTeCO291GkAlkIKAlXMq6knA0BBBCoR4AJ2PWocUy7AtEJOe3uxIcIJCDAROwEUDllIQSYeF2IMHtXSdoTbocsGh+SCbfj5VXpojeXV4WnsN4LzJ8/3/r162cTJkzwvi5UAIE0BMIk/JNPPmG+RBrgXKNqAdoTVVNlsmM0PgxzyiQMXBQBBOIWuPfee+2ZZ56J+7ScD4HcCmzbts2WLFlCIpHbCFMxBNIRIJlIx5mrIIBAwgJ62ZZWpNm5c2fCV+L0CPgvoOVglXzzxmv/Y0kNEMhagGQi6whwfQQQiE1g0qRJtnDhwtjOx4kQyKvAxo0bg+SbN17nNcLUC4H0BEgm0rPmSgggkLDAwIEDgyvQO5EwNKf3WiDslZg6darX9aDwCCDghgDJhBtxoBQIIBCTwPTp0+mdiMmS0+RTgF6JfMaVWiGQlQDJRFbyXBcBBBIRCNfLp3ciEV5O6rkAvRKeB5DiI+CgAMmEg0GhSAgg0JgAvRON+XF0fgXolchvbKkZAlkJkExkJc91EUAgMQH1Tmhi6ebNmxO7BidGwDcBeiV8ixjlRcAPAZIJP+JEKRFAoEYBTS6dNWuWqQHFhgACZuvWrbPx48cHiTYeCCCAQFwCvAE7LknOY9E3IkKCQNYCM2bMsP79+9uUKVOyLgrXRyBTAd52nSk/F69RgPZEjWAp7x6ND8lEygHI8+WiN1ee60rd/BCgAeVHnChl8gIk1skbc4X4BGhPxGeZxJmi8WGYUxLKnBMBBJwQ6Nq1q7388svBm36dKBCFQCADgcOHD9u2bdts4sSJGVydSyKAQN4FSCbyHmHqh0DBBcaOHRs0pPbt21dwCapfRAHNGVKvxKJFi6xTp05FJKDOCCCQsADJRMLAnB4BBLIVUANq+fLlNnv2bCZjZxsKrp6BgJaC1cpm4ftXMigCl0QAgZwLMGci5wFOs3rRMXRpXptrIdCRAGPGOxLi+7wJHD9+3Hr06GHHjh2z7t2756161CfHArQn3A5uND4kE27Hy6vSRW8urwpPYXMvoMnYd955p61Zs4alMXMfbSoogYceesg0zG/ChAmAIOCVAO0Jt8MVjQ/DnNyOF6VDAIGYBDQZe+7cucH4cd49ERMqp3FWoKWlJSgbiYSzIaJgCORGgJ6J3IQy+4pEM9XsS0QJEGgrwHCntiZ8ki8BhjflK55FrA3tCbejHo0PyYTb8fKqdNGby6vCU9jCCDDcqTChLmxFGd5U2NDnpuK0J9wOZTQ+DHNyO16UDgEEYhbQcCctkzl58mRWd4rZltNlL7B69eqgEAxvyj4WlACBogjQM1GUSKdQz2immsIluQQCdQssXbrUzp49azNnzqz7HByIgEsCejmdkuTXXnvNlDSzIeCrAO0JtyMXjQ89E27Hi9IhgEBCAg8++KDt3r3bNm/enNAVOC0C6Qlo+J4SCb1ThUQiPXeuhAACZvRMcBfEJhDNVGM7MSdCICGBcKLqoUOHWC42IWNOm46A5kkMGDDApk2bls4FuQoCCQrQnkgQN4ZTR+NDz0QMqJwCAQT8FNCLvHbs2MH8CT/DR6l/KxDOkyCR4JZAAIEsBOiZyEI9p9eMZqo5rSbVyqGA5k/s37/fVqxYkcPaUaU8C+zcudMef/xx5knkOcgFrBvtCbeDHo0PyYTb8fKqdNGby6vCU9jCCzBMpPC3gHcADNPzLmQUuEoB2hNVQmW0WzQ+DHPKKBBcFgEE3BJYvHixbdmyhQnZboWF0pQR0IRrLf+qYXp9+vQpsxcfI4AAAskLXJb8JbgCAggg4L5Ap06dTMOd1ED72te+ZsOGDXO/0JSwkAKfffaZPfHEEzZlyhTu00LeAVQaAbcEGObkVjy8Lk2028vrylD4wgrs27fPHn74YWtpaTFN0GZDwDUBhuS5FhHKE7cA7Ym4ReM9XzQ+DHOK15ezIYCA5wIDBw4M3pCtHgqNSWdDwCUB9Z5p03tS2BBAAAEXBEgmXIgCZUAAAacENMRp7ty5wZAnEgqnQlPowoSrjml+j4blsSGAAAIuCDDMyYUo5KQM0W6vnFSLahRYgMZbgYPvWNV1L2qBgLVr15JIOBYbihO/AO2J+E3jPGM0PvRMxKnLuRBAIFcCegmY3ir82GOPmSa9siGQhYASCb2YTn/SI5FFBLgmAghUEiCZqKTDdwggUHgBEorC3wKZAiiJ0P9YECDTMHBxBBCoIMAwpwo4fFWbQLTbq7aj2RsBtwUY8uR2fPJYurBHgkQij9GlTpUEaE9U0sn+u2h86JnIPiaUAAEEPBAo7aFgUrYHAfO8iCQSngeQ4iNQIAGSiQIFm6oigEBjAmFCwbKxjTlydGWBsBfstdde410nlan4FgEEHBBgmJMDQchLEaLdXnmpF/VAICqwefNmmzVrFuPYozD83pCAJvkvWrTI3n//fWP514YoOdhzAdoTbgcwGp/L3C4upUMAAQTcE2hubravfe1rwXso1PjTeynYEGhEQImEVg3TRiLRiCTHIoBA2gIMc0pbnOshgEAuBJRALF++3B5//HFTTwUbAvUKaA7OfffdFyxDvGLFCpZ/rReS4xBAIBMBhjllwp7Pi0a7vfJZS2qFwKUCaghqLsXo0aODPy/9lt8QqCywb98+e/jhh+3JJ58Meroq7823CBRDgPaE23GOxodkwu14eVW66M3lVeEpLAINCDBEpQG8Ah8azr1hqFyBbwKq3q4A7Yl2WZz5MBofhjk5ExoKggACvgrorcQanqK3ZY8cOdIOHz7sa1UodwoCSj7nz59vy5YtCybxM+cmBXQugQACiQmQTCRGy4kRQKBoAhrupKfMkydPZh5F0YJfZX01LE4Trc+cOWNr165l6dcq3dgNAQTcFWCYk7ux8a5k0W4v7ypAgRGISSCcR9GnTx+bM2cOE2pjcvX9NOGwJuZH+B5Jyp+0AO2JpIUbO380PvRMNObJ0QgggEAbge7duwdPnXv27MmwpzY6xfugdFjTmjVrmGhdvFuAGiOQawGSiVyHl8ohgEBWAppHoWFPWj5Ww55Wr15talSyFUtA82c0j0abhjWpt4oNAQQQyJMAw5zyFM2M6xLt9sq4OFweAWcETp8+bc8880wwMXvBggU0KJ2JTHIFUeK4bt06W7p0aZBQDhw4MLmLcWYEciZAe8LtgEbjQ8+E2/GidAggkAOBrl27mpKIRx55hF6KHMSzoyro3RHqjdDcmddff91IJDoS43sEEPBZgJ4Jn6PnWNmjmapjxaM4CDghEPZSbNu2jSfWTkQkvkIots8//7ytX7+e2MbHypkKKEB7wu2gR+NDMuF2vLwqXfTm8qrwFBaBlAX09Hr27NnBkCet7qPeCzZ/BVpaWoKhbJonM3HiRFbw8jeUlNwBAdoTDgShQhGi8WGYUwUsvkIAAQSSEtDQF03IHTp0qF111VVM0E4KOuHzKikcP3687dq1y7RS05QpU0gkEjbn9Agg4JYAPRNuxcPr0kQzVa8rQ+ERSFGgdHgM7yBIEb6BS2mVppUrVwaT6qdPn268xboBTA5FICJAeyIC4tiv0fiQTDgWIJ+LE725fK4LZUcgCwEaqFmo13bNaOI3duxYeiJqI2RvBDoUoD3RIVGmO0TjQzKRaTjydfHozZWv2lEbBNITCOdT6Io89U7PvdKVlES89NJLwXA09R6RRFTS4jsEGhOgPdGYX9JHR+PDnImkxTk/AgggUKOA5lNoRSAlEgsXLgzG5O/cuZOX3tXoGMfu6i2aP3++3XnnndatW7dgqdcJEyYk0hvx+ZvP2U1NTaZ/qC/+7/4WO6mKnGyx+0s/1883PWdvfh5HLTkHAgggUL8APRP123FkRCCaqUa+5lcEEKhTIBz+pOVk9VR81KhRrP5Up2W1hyl527Bhg4XmqfVEnN1qT/T7I1tg37EXti6y7/S74ssiX3jHfjj2Dntw87+2//SzH9rcO37XeCL4JQ8/5UeA9oTbsYzG5zK3i0vpEEAAAQT69OkTvPROScXmzZuD1Z+WLFlizc3NvE07xttDb63euHFjMJRJp1XP0Jw5cxLphShb7P9+xj48eb01vzDdHihNJHTAuRN26Bcn7foZa+xJEomyhHyBAALpCvBQI11vroYAAgjULaCkQu8x+OSTT4IhN5MnTw6GQCnBUEOYrT4BzVFZunSpde7c2d55550gcdMwM63Q1KlTp/pOWtdRF+zswT32U+tmA3td3abX4fO/32svn7zRvvXN37OS/oq6rsRBCCCAQFwC9EzEJcl5EEAAgZQE9II7jdvX/9QQfvXVV23MmDE2b948u+uuu0xzLtgqCxw/fty2bt1qetmcNr0fQklati8PPG17Nm22k9c325jB0ZcY/qO9t3+3vWuDbGb/aypXjm8RQACBFAWYM5Eidt4vFR1Dl/f6Uj8EXBLQakN79uyxdevW2f79+4PG8fDhw0ksSoKkBGL37t3BUKbQyKmhYhfnRARTrktKXvLjjQttzzt/bt/gUWAJCj/mTYD2hNsRjcaHZMLteHlVuujN5VXhKSwCORIoTSz0YjX1WIwcOdJuvvnmjJ+8p4+snpu333476IE4ceKE00nWhcM/tLF9Z5m9sNU2fqffpcOctJpTt3vspzN+Zu88ewfDnNK/lbhiigK0J1LEruNS0fgwZ6IORA5BAAEEXBbQUB09cV+xYkUwdGfw4MHBkqZXXXWVPfTQQ8EEYzWy8zjPQr0PmkOi5Vz1D94PfvCDIFQLFiwIeiU058TNYWCf20cHdttm62vfGtD90kTCwrkUzJdw+b87yoZAUQXoKC1q5Kk3AggUQiBMLJRczJw507Qi1IEDB4IXsOkdFlOnTrUBAwbYbbfdZl//+tete/fu3rgoGTp27FhQn127dgXLuOpdEKPKxuYjAAAGdUlEQVRHjw56YrKfA1EL5Rk7+PM9Ztc326Df6xw58Lz9/d7/ZidtkI1kvkTEhl8RQCBrAYY5ZR2BHF0/2u2Vo6pRFQRyKxAmF1rFSPMJ9G4FLYnas2fPYMWo/v3729VXX5358CiV89SpU/bRRx+ZEgf9HpZVZbz11luDMmc7gbqB2yR8v8S3XrYTL06w60tPFc6lsLl2aON3rA9jCkp1+DmHArQn3A5qND70TLgdL0qHAAIIJCqg5Wb1v3ArfdqvOQbhE/833ngj6MW48sorLyYaOkYN+XCrJ+lQUhBuYbKg33Vdbeo90aYelBtuuMH69etnkyZNChIcLd+aj+2svfOT/9N+pPdLjLzFrr2kUv9kJ7f92H60+aTduHCA9SaRuESHXxBAIHsBeiayj0FuShDNVHNTMSqCAAKBQNjwP3LkiJ07dy74n4ZMhZveFq2ko5ZNSYISFG1dunQJkgX93Lt37+C9Dz169Ej5XQ+1lD6GfX87sXp16amm/LZ34vM37bl+g236uyVfsppTCQY/5lWA9oTbkY3Gh2TC7Xh5VbrozeVV4SksAggggAACCDghQHvCiTCULUQ0PnSYlqXiCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgKXVfqS7xCoVaCpqanWQ9gfAQQQQAABBBBAwFMBkglPA+disVtbW10sFmVCAAEEEEAAAQQQSEiAYU4JwXJaBBBAAAEEEEAAAQTyLkAykfcIUz8EEEAAAQQQQAABBBISIJlICJbTIoAAAggggAACCCCQdwGSibxHmPohgAACCCCAAAIIIJCQAMlEQrCcFgEEEEAAAQQQQACBvAuQTOQ9wtQPAQQQQAABBBBAAIGEBEgmEoLltAgggAACCCCAAAII5F2AZCLvEaZ+CCCAAAIIIIAAAggkJEAykRAsp0UAAQQQQAABBBBAIO8CJBN5jzD1QwABBBBAAAEEEEAgIQGSiYRgOS0CCCCAAAIIIIAAAnkXIJnIe4SpHwIIIIAAAggggAACCQmQTCQEy2kRQAABBBBAAAEEEMi7AMlE3iNM/RBAAAEEEEAAAQQQSEiAZCIhWE6LAAIIIIAAAggggEDeBUgm8h5h6ocAAggggAACCCCAQEICJBMJwXJaBBBAAAEEEEAAAQTyLkAykfcIUz8EEEAAAQQQQAABBBISIJlICJbTIoAAAggggAACCCCQdwGSibxHmPohgAACCCCAAAIIIJCQwGXtnbepqam9j/kMAQQQQAABBBBAAAEEELgo0CaZaG1tvfglPyCAAAIIIIAAAggggAAC5QT+f5Yv0z+2hUJ/AAAAAElFTkSuQmCC"></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>x</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of \(n\left( {\left( {F \cup H} \right) \cap S'} \right)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br>