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<quiz>
  <question type="stack">
    <name>
      <text>Cartesian_Set_1</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>If \(X\), \(Y\) are sets containing \({@m@}\), \({@n@}\) elements respectively, how many elements are there in the cartesian product, \(X\times Y\), of the two sets?</p>
<p>\(| X \times Y| = \) [[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>The cartesian product of sets \(X\) and \(Y\), \(X \times Y\) is the set containing all ordered pairs with as first member an element of \(X\) and as second member an element of \(Y\). <br /> For each element of \(X\), one can construct \({@n@}\) different pairs, with \({@n@}\) being the number of elements in \(Y\). Since there are \({@m@}\) elements in \(X\), this will mean a total of \({@m@}*{@n@}\) pairs. <br /> Hence the cardinality of \(X \times Y\) is \({@m*n@}\).</p>]]></text>
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      <text/>
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    <questionvariables>
      <text>m:rand_with_step(2, 9, 1);
 n:rand_with_step(2, 9, 1);
 correctanswer:m*n;</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:result]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\(| X \times Y| = \) \({@m@} * {@n@}\) elements = \({@correctanswer@}\)</text>
    </questionnote>
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      <text/>
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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>
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      <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>
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        <name>ans1</name>
        <value>correctanswer-1</value>
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  </question>
</quiz>
