Project ForgeDiscrete Mathematics
Propositional Logic
GATE 2012
Medium
Consider the following logical inferences.
I1: If it rains then the cricket match will not be played. The cricket match was played. Inference: There was no rain.
I2: If it rains then the cricket match will not be played. It did not rain. Inference: The cricket match was played.
Which of the following is TRUE?
- ABoth I1 and I2 are correct inferences
- I1 is correct but I2 is not a correct inference
- CI1 is not correct but I2 is a correct inference
- DBoth I1 and I2 are not correct inferences
Explanation
I1 has the form P→¬Q, Q ⊢ ¬P — this is modus tollens (denying the consequent), a logically valid inference. I2 has the form P→¬Q, ¬P ⊢ Q — this is the fallacy of denying the antecedent, which is NOT valid (¬P tells us nothing about Q). So I1 is correct but I2 is not.
Source: GATE CS 2012 (2012)
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