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<quiz>
  <question type="stack">
    <name>
      <text>35.1.4.6 Complement, union, intersection exercise (Exercise 4(c)(d)(f)(g)) (NOT IN QUIZ)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>Let \(A = {@A@}\), \(B = {@B@}\), and \(S = {@S@}\) the universal set. Recall that the complement of \(A\) is denoted by \(A'\) and the complement of \(B\) is denoted by \(B'\). List the elements of each of the following sets.</p>
<ol class="HELM_parts">
<li>\(A' \cup B' = \) [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</li>
<li>\(A' \cap B' = \) [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</li>
<li>\((A \cup B)' = \) [[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</li>
<li>\((A \cap B)' = \) [[input:ans4]] [[validation:ans4]] [[feedback:prt4]]</li>
</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>We are given \(A = {@A@}\), \(B = {@B@}\), and \(S = {@S@}\) the universal set.</p>
<p>We have \(A' = {@AA@}\) and \(B' = {@BB@}\), so</p> 
<p>(a) \(A' \cup B' = {@ta1@}\),</p> 
<p>(b) \(A' \cap B' = {@ta2@}\).</p>
<p>(c) We have \(A \cup B = {@C@}\), so \[(A \cup B)' = {@ta3@}.\]</p>
<p>(d) We have \(A \cap B = {@D@}\), so \[(A \cap B)' = {@ta4@}.\]</p>
<p>Note that the answers for (a) and (d) are the same. Also, the answers for (b) and (c) are the same.</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2020070100</text>
    </stackversion>
    <questionvariables>
      <text>a:rand([8,9,10,11,12]);
L:makelist(i,i,0,a);
even:sublist(L,evenp);
odd:sublist(L,oddp);
S:setify(L);
A1:setify(rand_selection(even,1));
A2:setify(rand_selection(odd,3));
A:union(A1,A2);
B:setify(even);
AA:setdifference(S,A);
BB:setdifference(S,B);
C:union(A,B);
D:intersection(A,B);
ta1:union(AA,BB);
ta2:intersection(AA,BB);
ta3:setdifference(S,C);
ta4:setdifference(S,D);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[A = {@A@}, \quad B = {@B@}, \quad S = {@S@}\]
\[ A' \cup B' ={@ta1@}, \quad A' \cap B' = {@ta2@} \]
\[(A \cup B)' = {@ta3@}, \quad (A \cap B)' = {@ta4@} \]</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
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    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
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      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta1</tans>
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    </input>
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      </testinput>
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        <name>ans2</name>
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        <name>ans3</name>
        <value>ta3</value>
      </testinput>
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        <value>ta4</value>
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    </qtest>
  </question>
</quiz>
