1 vote

Consider the following logical inferences :

$I_{1}$ : If it is Sunday then school will not open.

The school was open.

Inference : It was not Sunday.

$I_{2}$ : If it is Sunday then school will not open.

It was not Sunday.

Inference : The school was open.

Which of the following is correct ?

- Both $I_{1}$ and $I_{2}$ are correct inferences.
- $I_{1}$ is correct but $I_{2}$ is not a correct inference.
- $I_{1}$ is not correct but $I_{2}$ is a correct inference.
- Both $I_{1}$ and $I_{2}$ are not correct inferences.

3 votes

p: it is sunday q: school will open

so If it is Sunday then school will not open is represented as

p-->~q so it can imply q->~p (by contrapositive) so first inference is correct

for second

If it is Sunday then school will not open is represented as

p-->~q

given ~p so it can not imply ~p-->q (inverse impliation) unless its converse(~q->p ) is true which is not true here

note only contapositive holds true in all cases