<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>parsons proof 2-Interchangable order</text>
    </name>
    <questiontext format="moodle_auto_format">
      <text><![CDATA[<p>Let \(n\in\mathbb{N}\).  Show that \(n\) is odd if and only if \(n^2\) is odd. </p>
[[parsons input="ans1"]]
{# parsons_encode(proof_steps) #}
[[/parsons ]]
<p>[[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="moodle_auto_format">
      <text><![CDATA[This is the proof, written with some structure
{@proof_display(tal[2], proof_steps)@}
Notice this proof has two sub-proofs, which can occur in any order.  Therefore we have two correct versions of this proof.
<table><tr>
<td><div class="proof">{@proof_display_para(tal[1], proof_steps)@}</div></td>
<td><div class="proof">{@proof_display_para(tal[2], proof_steps)@}</div></td>
</tr></table>
Can you see the differences between these proofs?]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2024092500</text>
    </stackversion>
    <questionvariables>
      <text><![CDATA[stack_include_contrib("prooflib.mac");

ta: proof_iff(proof("assodd","defn_odd","alg_odd","def_M_odd","conc_odd"), proof("contrapos","assnotodd","even","alg_even","def_M_even","conc_even"));

proof_steps: [
    ["assodd",     "Assume that \\(n\\) is odd."],
    ["defn_odd",   "Then there exists an \\(m\\in\\mathbb{Z}\\) such that \\(n=2m+1\\)."],
    ["alg_odd",    "\\[ n^2 = (2m+1)^2 = 2(2m^2+2m)+1.\\]"],
    ["def_M_odd",  "Define \\(M=2m^2+2m\\in\\mathbb{Z}\\) then \\(n^2=2M+1\\)."],
    ["conc_odd",   "Hence \\(n^2\\) is odd."],

    ["contrapos",  "We reformulate \"\\(n^2\\) is odd \\(\\Rightarrow \\) \\(n\\) is odd \" as the contrapositive."],
    ["assnotodd",  "Assume that \\(n\\) is not odd."],
    ["even",       "Then \\(n\\) is even, and so there exists an \\(m\\in\\mathbb{Z}\\) such that \\(n=2m\\)."],
    ["alg_even",   "\\[ n^2 = (2m)^2 = 2(2m^2).\\]"],
    ["def_M_even", "Define \\(M=2m^2\\in\\mathbb{Z}\\) then \\(n^2=2M\\)."],
    ["conc_even",  "Hence \\(n^2\\) is even."]
];

/* Permute the steps randomly. */ 
proof_steps: random_permutation(proof_steps);

/* Generate the alternative proofs. */
tal: proof_alternatives(ta);

/* Create a set of flattened proofs. */
tas: setify(map(proof_flatten, tal));]]></text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote format="html">
      <text>{@ map(first, proof_steps) @}</text>
    </questionnote>
    <questiondescription format="html">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <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>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans1</name>
      <type>parsons</type>
      <tans>[ta, proof_steps]</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>0</mustverify>
      <showvalidation>0</showvalidation>
      <options/>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text>sa: parsons_decode(ans1);
check: elementp(sa,tas);</text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>check</sans>
        <tans>true</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>263493547</deployedseed>
    <deployedseed>2080086703</deployedseed>
    <deployedseed>2119685624</deployedseed>
    <deployedseed>2065386162</deployedseed>
    <deployedseed>1272837801</deployedseed>
    <deployedseed>2105511895</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description>Test case assuming the teacher's input gets full marks.</description>
      <testinput>
        <name>ans1</name>
        <value>apply(parsons_answer,[ta, proof_steps])</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
