Consider the following logical inferences : I1 : If it is Sunday then school…
2016
Consider the following logical inferences :
I1 : If it is Sunday then school will not open.
The school was open. Inference :
It was not Sunday.
I2 : If it is Sunday then school will not open.
It was not Sunday. Inference :
The school was open.
Which of the following is correct ?
- A.
Both I1 and I2 are correct inferences.
- B.
I1 is correct but I2 is not a correct inference.
- C.
I1 is not correct but I2 is a correct inference.
- D.
Both I1 and I2 are not correct inferences.
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Correct answer: B
Key idea: A conditional statement 'If it is Sunday then school will not open' can be written as 'If Sunday (S) then not Open (¬O)'. A conditional is logically equivalent to its contrapositive.
Evaluation of the first inference: From 'If it is Sunday then school will not open' and 'The school was open' we use the contrapositive (If the school is open then it is not Sunday). Therefore you can validly conclude it was not Sunday. The first inference is valid.
Evaluation of the second inference: From 'If it is Sunday then school will not open' and 'It was not Sunday' you cannot deduce 'The school was open'. The falsity of the antecedent does not force the truth of the consequent. Counterexample: it could be a Monday when the school is closed; both premises are true but the conclusion is false. So the second inference is invalid.
Conclusion: Only the first inference is correct; the second inference is not valid.
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