# UGCNET-AUG2016-III: 74

1 vote
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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 ?

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

recategorized

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

### here ans is B

note only contapositive holds true in all cases

I.                (p->!q) ^q ---->  !p( holds good)                        (T--->F will never occur)

||               {(p->!q) ^!p] ----> q (doesn't hold good)          (T--->F will occur)

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