Skip to content
This repository
Fetching contributors…

Cannot retrieve contributors at this time

file 172 lines (154 sloc) 10.825 kb
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172
<!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>
Something went wrong with that request. Please try again.