# publicKhan/khan-exercises

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 ``` 9d9ca185 » xymostech ``` 2012-05-24 Added an exercise about detachment and syllogism 1 2 3 4 5 Logical arguments and deductive reasoning 6 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]] ``` 3980c112 » divad12 ``` 2012-05-26 Fix capitalization bug with "logical arguments..." exercise 41 (TYPE === 1 || TYPE === 2) ? "No logical conclusion possible" : capitalize(CONCLUSION[TYPE]) ``` 9d9ca185 » xymostech ``` 2012-05-24 Added an exercise about detachment and syllogism 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

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• 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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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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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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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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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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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"]], ``` 33cb3832 » xymostech ``` 2012-05-29 Fix typos in logical arguments 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"]], ``` 9d9ca185 » xymostech ``` 2012-05-24 Added an exercise about detachment and syllogism 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

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• If HYP_A, then CONC_B.
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• If HYP_A, then HYP_B.
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• If CONC_A, then CONC_B.
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• 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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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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No. So, we cannot form a logical conclusion.

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