Consider the following logical inferences. I1: If it rains then the cricket…
2012
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?
- 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
Attempted by 51 students.
Show answer & explanation
Correct answer: B
Answer: The first inference is valid and the second is not.
Why the first inference is valid:
Original statement: If it rains then the cricket match will not be played.
This has the logical form: If R then not P (R → ¬P).
The contrapositive of R → ¬P is P → ¬R, so observing that the match was played (P) lets us conclude there was no rain (¬R).
Why the second inference is invalid:
From R → ¬P and ¬R you cannot conclude P. This is the logical fallacy called denying the antecedent.
Counterexample: Even if it did not rain, the match could still be cancelled for other reasons (for example, poor light or an unrelated emergency), so ¬R does not guarantee P.
Conclusion: The inference that the match being played implies there was no rain is valid; the inference that no rain implies the match was played is invalid. Therefore the correct choice is the one stating that the first inference is correct but the second is not.
A video solution is available for this question — log in and enroll to watch it.