<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="multichoice">
    <name>
      <text>3.0.6 (What can we deduce?)</text>
    </name>
    <questiontext format="moodle_auto_format">
      <text><![CDATA[<p>Suppose that we have the following three facts.</p>
<ol>
<li>Alice will be admitted to university only if she is clever.</li>
<li>If Alice is clever then she does not need to work hard</li>
<li>Alice has to work hard.</li>
</ol>

<p>By forming a chain of logical implications, which of the following is the final conclusion that we can deduce from these statements?</p>]]></text>
    </questiontext>
    <generalfeedback format="moodle_auto_format">
      <text><![CDATA[<p>Set \(A, B\) and \(C\) to be the statements:</p>
<ul style="list-style: none;">
<li>A: Alice is admitted to university.</li>
<li>B: Alice is clever.</li>
<li>C: Alice works hard.</li>
</ul>

<p>Then statement 1. says \(A\) implies \(B\), statement 2. says \(B\) implies \(C\) is false (called the complement of C, often denoted \(\bar{C}\)). Statement 3. tells us that \(C\) is true. Therefore
\[
C \mbox{ implies } \bar{B} \qquad \mbox{and} \qquad \bar{B} \mbox{ implies } \bar{A}.
\]
Therefore we can deduce that Alice will not be admitted to university.</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.3333333</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <single>true</single>
    <shuffleanswers>true</shuffleanswers>
    <answernumbering>none</answernumbering>
    <showstandardinstruction>0</showstandardinstruction>
    <correctfeedback format="html">
      <text>Your answer is correct.</text>
    </correctfeedback>
    <partiallycorrectfeedback format="html">
      <text>Your answer is partially correct.</text>
    </partiallycorrectfeedback>
    <incorrectfeedback format="html">
      <text>Your answer is incorrect.</text>
    </incorrectfeedback>
    <shownumcorrect/>
    <answer fraction="100" format="html">
      <text>Alice will not be admitted into university.</text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text>Alice is clever.</text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text>Alice does not work hard.</text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text>Alice works hard.</text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text>Alice will be admitted into university</text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text>Alice is not clever.</text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
  </question>
</quiz>
