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Consider the following logical inferences.

$I_{1}$: If it rains then the cricket match will not be played.
The cricket match was played.
Inference:  There was no rain.

$I_{2}$: 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 $I_{1}$ and $I_{2}$ are correct inferences
(B) $I_{1}$ is correct but $I_{2}$ is not a correct inference
(C) $I_{1}$ is not correct but $I_{2}$ is a correct inference
(D) Both $I_{1}$ and $I_{2}$ are not correct inferences
edited | 1.2k views

$I_1$ is a correct inference. $I_2$ is not a correct inference as it was not mentioned what would have happened if it hadn't rained- They might have played or they might not have played.
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This is an example of Modus tollen. Isn't it ?
yes it is example of modus tollens

Only I1 is example of Modus Tollen. I2 does not look like Modus Tollen. Pooja Palod mam. please confirm.

Let us assume p=It rains,q=cricket match will not be played.

I1: If it rains then the cricket match will not be played   (p->q)

The cricket match was played. (~q)
Inference:  There was no rain.(~p)

p->q

~q

~p    (Modus tollens )

Thus I1 is an inferenece.

I2:can be written as

p->q

~p

~q

Not an inference.