# Khan/khan-exercises

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 9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 24, 2012 1 cde9e9f Re-run the exercises through the updated cleaner. jeresig authored Apr 24, 2013 2 3 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 4 9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 5 Logical arguments and deductive reasoning ac1415e Use requirejs for module loading spicyj authored Mar 5, 2014 6 9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 7 8 9
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13 14 [[person(1)+" misses the bus", he(1)+" will be late for school", 15 [person(1)+" missed the bus", 16 person(1)+" is late for school", 17 person(1)+" did not miss the bus", 18 person(1)+" is not late for school"]], 19 ["it is Tuesday", "I will have a hamburger for lunch", 20 ["it is Tuesday", 21 "I will have a hamburger for lunch today", 22 "it is not Tuesday", 23 "I will not have a hamburger for lunch today"]], 24 ["Wiggles are walking", "Tiggles are talking", 25 ["Wiggles are walking", 26 "Tiggles are talking", 27 "Wiggles are not walking", 28 "Tiggles are not talking"]], 29 ["I go to practice today", "I will play in the game tomorrow", 30 ["I went to practice today", 31 "I will play in the game tomorrow", 32 "I did not go to practice today", 33 "I will not play in the game tomorrow"]]] 34 35 randRange(0, QUESTIONS.length - 1) 36 QUESTIONS[Q_TYPE][0] 37 QUESTIONS[Q_TYPE][1] 38 randRange(0, 3) 39 QUESTIONS[Q_TYPE][2] 40 [IMPLICATION[1], IMPLICATION[0], IMPLICATION[3], IMPLICATION[2]] 3980c11 Fix capitalization bug with "logical arguments..." exercise divad12 authored May 26, 2012 41 (TYPE === 1 || TYPE === 2) ? "No logical conclusion possible" : capitalize(CONCLUSION[TYPE]) 9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 42
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Use the given information to make a logical conclusion, if possible. If a logical conclusion is not possible, choose "no logical conclusion possible."

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If IF_CLAUSE, then THEN_CLAUSE. capitalize(IMPLICATION[ TYPE ]).

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SOLUTION

0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 46
9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 47
• capitalize(CONCLUSION[TYPE])
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• No logical conclusion possible
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Identify the hypothesis, the conclusion of the first sentence, and the second sentence.

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Does the second sentence refer to the hypothesis of the first sentence, or the conclusion of the first sentence?

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The second sentence refers to the hypothesis of the first sentence, because they both talk about whether or not IMPLICATION[0].

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Does the second sentence state the hypothesis, or the opposite of the hypothesis?

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e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 64
9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 65

The second sentence refers to the conclusion of the first sentence, because they both talk about whether or not IMPLICATION[1].

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Does the second sentence state the conclusion, or the opposite of the conclusion?

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e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 68
9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 69

The second sentence states the hypothesis of the first sentence.

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Because the second sentence states the hypothesis of the first sentence, the second sentence implies the first sentence.

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Since we are implying the original statement, we can conclude the conclusion of the first statement.

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e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 73
9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 74

The second sentence states the conclusion of the first sentence.

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Because the second sentence states the conclusion of the first sentence, the second sentence implies the converse of the first sentence.

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Converses are not logically equivalent to their original statements, so we cannot form a logical conclusion.

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e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 78
9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 79

The second sentence states the opposite of the hypothesis of the first sentence.

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Because the second sentence states the opposite of the hypothesis of the first sentence, the second sentence implies the inverse of the first sentence.

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Inverses are not logically equivalent to their original statements, so we cannot form a logical conclusion.

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e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 83
9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 84

Because the second sentence states the opposite of the conclusion of the first sentence, the second sentence implies the contrapositive of the first sentence.

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Since the contrapositive is implied by the first sentence, the second sentence implies the opposite of the hypothesis.

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92 93 [[true, true, ["a figure is a square", "it is a rectangle", "a figure is a rectangle", "it has four right angles"]], 94 [false, true, ["you play basketball", "you are athletic", "you play volleyball", "you are athletic"]], 95 [true, true, ["it is Saturday", "you don't have to go to school", "you don't have to go to school", "you can play in the park"]], 33cb383 Fix typos in logical arguments xymostech authored May 29, 2012 96 [false, true, ["you live in Los Angeles", "you live in California", "you live in Sacramento", "you live in California"]], 97 [true, true, ["a ray bisects an angle", "it creates two congruent angles", "there are two congruent angles", "the two angles have the same measure"]], 9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 98 [false, false, ["a shape is a pentagon", "the shape has five sides", "a shape is a pentagon", "the shape has five angles"]], 99 [true, true, ["a student is in the twelfth grade", "he or she is in high school", "a student is in high school", "he or she is not in college"]], 100 [false, true, ["you have a picnic", "you will see ants", "it rains a lot", "you will see ants"]]] 101 randRange(0, QUESTIONS.length - 1) 102 QUESTIONS[Q_TYPE][0] 103 QUESTIONS[Q_TYPE][1] 104 QUESTIONS[Q_TYPE][2][0] 105 QUESTIONS[Q_TYPE][2][1] 106 QUESTIONS[Q_TYPE][2][2] 107 QUESTIONS[Q_TYPE][2][3] 108 CONC_POSSIBLE ? ("If "+HYP_A+", then "+CONC_B+".") : "No logical conclusion possible." 109
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Use the given information to make a logical conclusion, if possible.

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If HYP_A, then CONC_A. If HYP_B, then CONC_B.

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SOLUTION

0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 113
9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 114
• If HYP_A, then CONC_B.
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• If HYP_A, then HYP_B.
• e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 116
• If CONC_A, then CONC_B.
• 9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 117
• No logical conclusion possible.
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Identify the first hypothesis, the first conclusion, the second hypothesis, and the second conclusion.

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123 \$( "#hyp_a" ).addClass( "hint_blue" ); 124 \$( "#conc_a" ).addClass( "hint_green" ); 125 \$( "#hyp_b" ).addClass( "hint_red" ); 126 \$( "#conc_b" ).addClass( "hint_purple" ); 127
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Do the two sentences come in the form "If P, then Q. If Q, then R", where first conclusion and second hypothesis are the same?

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In other words, do the sentences look like \blue{P}\implies \green{Q}. \red{Q}\implies \purple{R}?

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e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 133
9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 134

Yes. Because the middle two statements both say HYP_B, we can chain the statements together: \blue{P}\implies\green{Q}\implies\purple{R} or "HYP_A"\implies"CONC_A"\implies"CONC_B".

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We can now remove the middle statement, and arrive at the conclusion "HYP_A"\implies"CONC_B". So, the answer is "If HYP_A, then CONC_B."

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e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 137

No. So, we cannot form a logical conclusion.

9d9ca18 Added an exercise about detachment and syllogism xymostech authored May 25, 2012 138
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cde9e9f Re-run the exercises through the updated cleaner. jeresig authored Apr 24, 2013 142 143
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