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<!DOCTYPE html>
<html data-require="math word-problems">
<head>
<title>Converse, inverse, and contrapositive</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="TYPE">randFromArray([ 'converse', 'inverse', 'contrapositive' ])</var>
</div>
<div class="problems">
<div id="rain-and-soccer-practice">
<div class="vars">
<var id="CHOICES">{
"converse" : "If soccer practice will be canceled today, then it will rain.",
"inverse" : "If it does not rain today, soccer practice will not be canceled.",
"contrapositive" : "If soccer practice is not canceled today, then it is not raining.",
"other1" : "If I don't like soccer, then I won't go to soccer practice.",
"other2" : "When it rains I don't want to go to soccer practice." }
</var>
<var id="HYPOTHESIS">"it rains today"</var>
<var id="NEG_HYPOTHESIS">"it does not rain today"</var>
<var id="CONCLUSION">"soccer pratice will be canceled"</var>
<var id="NEG_CONCLUSION">"soccer pratice will not be canceled"</var>
</div>
<p class="problem">Identify the <strong><var>TYPE</var></strong> of the given conditional statement.</p>
<p class="question">"If it rains today, soccer practice will be canceled."</p>
<p class="solution"><var>CHOICES[TYPE]</var></p>
<ul class="choices" data-show="4" data-none="true">
<li data-each="CHOICES as key, value"><var>value</var></li>
</ul>
</div>
<div id="sun-and-hat" data-type="rain-and-soccer-practice">
<div class="vars">
<var id="CHOICES">{
"converse" : "If I need to wear a hat today, then the sun is bright outside.",
"inverse" : "The sun is not bright outside, so I do not need to wear a hat.",
"contrapositive" : "If I am not wearing a hat today, then the sun is not bright outside.",
"other1" : "I only wear hats when it rains.",
"other2" : "If I do not wear a hat today, then I could get sunburned." }
</var>
<var id="HYPOTHESIS">"the sun is bright outside today"</var>
<var id="NEG_HYPOTHESIS">"the sun is not bright outside today"</var>
<var id="CONCLUSION">"I will wear a hat"</var>
<var id="NEG_CONCLUSION">"I will not wear a hat"</var>
</div>
<p class="question">"The sun is bright outside today, so I will wear a hat."</p>
</div>
<div id="dessert-and-pie" data-type="rain-and-soccer-practice">
<div class="vars">
<var id="CHOICES">{
"converse" : "If I eat apple pie, then we will have dessert tonight.",
"inverse" : "If we do not have dessert tonight, then I will not eat apple pie.",
"contrapositive" : "If I did not eat apple pie, then we did not have dessert tonight.",
"other1" : "If we do not have dessert tonight, I will be upset.",
"other2" : "I do not like apple pie, so I will not eat dessert tonight." }
</var>
<var id="HYPOTHESIS">"we have dessert tonight"</var>
<var id="NEG_HYPOTHESIS">"we do not have dessert tonight"</var>
<var id="CONCLUSION">"I will eat apple pie"</var>
<var id="NEG_CONCLUSION">"I will not eat apple pie"</var>
</div>
<p class="question">"If we have dessert tonight, I will eat apple pie."</p>
</div>
<div id="vertical-and-congruent-angles" data-type="rain-and-soccer-practice">
<div class="vars">
<var id="CHOICES">{
"converse" : "All pairs of congruent angles are vertical angles.",
"inverse" : "All pairs of angles that are not vertical angles are not congruent angles.",
"contrapositive" : "All pairs of angles that are not congruent are not vertical angles.",
"other1" : "Vertical angles are always congruent.",
"other2" : "Congruent angles can be vertical angles but they don't have to be." }
</var>
<var id="HYPOTHESIS">"a pair of angles are vertical angles"</var>
<var id="NEG_HYPOTHESIS">"a pair of angles are not vertical angles"</var>
<var id="CONCLUSION">"the two angles are congruent"</var>
<var id="NEG_CONCLUSION">"the two angles are not congruent"</var>
</div>
<p class="question">"All pairs of vertical angles are congruent angles."</p>
</div>
<div id="elephants-and-peanuts" data-type="rain-and-soccer-practice">
<div class="vars">
<var id="CHOICES">{
"converse" : "If an animal eats peanuts, then it is an elephant.",
"inverse" : "If an animal is not an elephant, then it does not eat peanuts.",
"contrapositive" : "If an animal does not eat peanuts, then it is not an elephant.",
"other1" : "Elephants also eat hay.",
"other2" : "Animals that eat peanuts may also like peanut butter." }
</var>
<var id="HYPOTHESIS">"an animal is an elephant"</var>
<var id="NEG_HYPOTHESIS">"an animal is not an elephant"</var>
<var id="CONCLUSION">"the animal eats peanuts"</var>
<var id="NEG_CONCLUSION">"the animal does not eat peanuts"</var>
</div>
<p class="question">"Elephants eat peanuts."</p>
</div>
<div id="equations-and-equations" data-type="rain-and-soccer-practice">
<p class="question">"If <code>3x+1=7</code>, then <code>x=2</code>."</p>
<p class="solution">
<span data-if="TYPE === 'converse'">If <code>x=2</code>, then <code>3x+1=7</code>.</span>
<span data-if="TYPE === 'inverse'">If <code>3x+1\not=7</code>, then <code>x\not=2</code>.</span>
<span data-if="TYPE === 'contrapositive'">If <code>x\not=2</code>, then <code>3x+1\not=7</code>.</span>
</p>
<ul class="choices" data-show="4" data-none="true">
<li>If <code>x=2</code>, then <code>3x+1=7</code>.</li>
<li>If <code>3x+1\not=7</code>, then <code>x\not=2</code>.</li>
<li>If <code>x\not=2</code>, then <code>3x+1\not=7</code>.</li>
<li>If <code>x=4</code>, then <code>3x+1=13</code>.</li>
<li>If <code>3x+1=10</code>, then <code>x=3</code>.</li>
</ul>
<div class="hints">
<p>
In this statement, the hypothesis is <strong><span class="hint_green"><code>3x+1=7</code></span></strong> and the conclusion is <strong><span class="hint_blue"><code>x=2</code></span></strong>
</p>
<p data-if="TYPE === 'converse'">
Thus, when we take the converse, the hypothesis becomes <strong><span class="hint_blue"><code>x=2</code></span></strong> and the conclusion becomes <strong><span class="hint_green"><code>3x+1=7</code></span></strong>.
</p>
<p data-if="TYPE === 'inverse'">
Thus, when we take the inverse, the hypothesis becomes <strong><span class="hint_green"><code>3x+1\not=7</code></span></strong> and the conclusion becomes <strong><span class="hint_blue"><code>x\not=2</code></span></strong>.
</p>
<p data-if="TYPE === 'contrapositive'">
Thus, when we take the contrapositive, the hypothesis becomes <strong><span class="hint_blue"><code>x\not=2</code></span></strong> and the conclusion becomes <strong><span class="hint_green"><code>3x+1\not=7</code></span></strong>.
</p>
<p>
Bringing the hypothesis and conclusion together, we find the <var>TYPE</var> of the original statement to be, <strong>
<span data-if="TYPE === 'converse'">"If <code>x=2</code>, then <code>3x+1=7</code>."</span>
<span data-if="TYPE === 'inverse'">"If <code>3x+1\not=7</code>, then <code>x\not=2</code>."</span>
<span data-if="TYPE === 'contrapositive'">"If <code>x\not=2</code>, then <code>3x+1\not=7</code>."</span>
</strong>
</p>
</div>
</div>
</div>
<div class="hints">
<p>
In this statement, the hypothesis is <strong>"<span class="hint_green"><var>HYPOTHESIS</var></span>"</strong> and the conclusion is <strong>"<span class="hint_blue"><var>CONCLUSION</var></span>"</strong>
</p>
<p data-if="TYPE === 'converse'">
Thus, when we take the converse, the hypothesis becomes <strong>"<span class="hint_blue"><var>CONCLUSION</var></span>"</strong> and the conclusion becomes <strong>"<span class="hint_green"><var>HYPOTHESIS</var></span>"</strong>.
</p>
<p data-if="TYPE === 'inverse'">
Thus, when we take the inverse, the hypothesis becomes <strong>"<span class="hint_green"><var>NEG_HYPOTHESIS</var></span>"</strong> and the conclusion becomes <strong>"<span class="hint_blue"><var>NEG_CONCLUSION</var></span>"</strong>.
</p>
<p data-if="TYPE === 'contrapositive'">
Thus, when we take the contrapositive, the hypothesis becomes <strong>"<span class="hint_blue"><var>NEG_CONCLUSION</var></span>"</strong> and the conclusion becomes <strong>"<span class="hint_green"><var>NEG_HYPOTHESIS</var></span>"</strong>.
</p>
<p>
Bringing the hypothesis and conclusion together, we find the <var>TYPE</var> of the original statement to be, <strong>"<var>CHOICES[TYPE]</var>"</strong>
</p>
</div>
</div>
</body>
</html>
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