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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.
in Discrete Mathematics
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3 Answers

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

here ans is B 

note only contapositive holds true in all cases

0 votes
Answer is B
0 votes
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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