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 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 `        Logical arguments and deductive reasoning

[[person(1)+" misses the bus", he(1)+" will be late for school",                            [person(1)+" missed the bus",                             person(1)+" is late for school",                             person(1)+" did not miss the bus",                             person(1)+" is not late for school"]],                         ["it is Tuesday", "I will have a hamburger for lunch",                            ["it is Tuesday",                             "I will have a hamburger for lunch today",                             "it is not Tuesday",                             "I will not have a hamburger for lunch today"]],                         ["Wiggles are walking", "Tiggles are talking",                            ["Wiggles are walking",                             "Tiggles are talking",                             "Wiggles are not walking",                             "Tiggles are not talking"]],                         ["I go to practice today", "I will play in the game tomorrow",                             ["I went to practice today",                              "I will play in the game tomorrow",                              "I did not go to practice today",                              "I will not play in the game tomorrow"]]]                                        randRange(0, QUESTIONS.length - 1)                    QUESTIONS[Q_TYPE][0]                    QUESTIONS[Q_TYPE][1]                    randRange(0, 3)                    QUESTIONS[Q_TYPE][2]                    [IMPLICATION[1], IMPLICATION[0], IMPLICATION[3], IMPLICATION[2]]                    (TYPE === 1 || TYPE === 2) ? "No logical conclusion possible" : capitalize(CONCLUSION[TYPE])

Use the given information to make a logical conclusion, if possible. If a logical conclusion is not possible, choose "no logical conclusion possible."

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

SOLUTION

• capitalize(CONCLUSION[TYPE])
•
• No logical conclusion possible
•

Identify the hypothesis, the conclusion of the first sentence, and the second sentence.

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

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

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

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

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

The second sentence states the hypothesis of the first sentence.

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

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

The second sentence states the conclusion of the first sentence.

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

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

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

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

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

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

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

[[true, true, ["a figure is a square", "it is a rectangle", "a figure is a rectangle", "it has four right angles"]],                         [false, true, ["you play basketball", "you are athletic", "you play volleyball", "you are athletic"]],                         [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"]],                         [false, true, ["you live in Los Angeles", "you live in California", "you live in Sacramento", "you live in California"]],                         [true, true, ["a ray bisects an angle", "it creates two congruent angles", "there are two congruent angles", "the two angles have the same measure"]],                         [false, false, ["a shape is a pentagon", "the shape has five sides", "a shape is a pentagon", "the shape has five angles"]],                         [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"]],                         [false, true, ["you have a picnic", "you will see ants", "it rains a lot", "you will see ants"]]]                    randRange(0, QUESTIONS.length - 1)                    QUESTIONS[Q_TYPE][0]                    QUESTIONS[Q_TYPE][1]                    QUESTIONS[Q_TYPE][2][0]                    QUESTIONS[Q_TYPE][2][1]                    QUESTIONS[Q_TYPE][2][2]                    QUESTIONS[Q_TYPE][2][3]                    CONC_POSSIBLE ? ("If "+HYP_A+", then "+CONC_B+".") : "No logical conclusion possible."

Use the given information to make a logical conclusion, if possible.

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

SOLUTION

• If HYP_A, then CONC_B.
•
• If HYP_A, then HYP_B.
•
• If CONC_A, then CONC_B.
•
• No logical conclusion possible.
•

Identify the first hypothesis, the first conclusion, the second hypothesis, and the second conclusion.

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?

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

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".

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."

No. So, we cannot form a logical conclusion.

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