GATE CSE 2015 Set 3 | Question: GA-6

Question

Alexander turned his attention towards India, since he had conquered Persia.

Which one of the statements below is logically valid and can be inferred from the above sentence?

• A. Alexander would not have turned his attention towards India had he not conquered Persia.
• B. Alexander was not ready to rest on his laurels, and wanted to march to India.
• C. Alexander was not completely in control of his army and could command it to move towards India.
• D. Since Alexander's kingdom extended to Indian borders after the conquest of Persia, he was keen to move further.

Comments

Why not (B) ?

Answer 1

Answer should be A as other options required more information

Let $P$ be "Alexander turned his attention towards India " and $Q$ be "he had conquered Persia"

$P\text{  since }Q  \equiv  (\neg Q \implies \neg P)$

$\neg P$ is "Alexander would not have turned his attention towards India"

$\neg Q$ is "he had not conquered Persia"

Comments

Srijay Deshpande    @Arjun Sir

Please clear me on one thing - whether ( p since q) , is p->q or q->p.

Here ,I think that the statement is like-

If  Alexender has conquered Persia , then he will conquer India.  P->I

NotI -> Not P

Thus, Alexender will not conquer India ,had he not conquered Persia.

 Is It correct  Sir ?

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I also have same doubt.

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P since Q ≡ (¬Q⟹¬P)

(¬Q⟹¬P) is contrapositive so equivalent to P->Q

So  (¬Q⟹¬P)  ≡ P->Q

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Very good explanation

Answer 2

answer is d

Comments

please explain why d

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@Naresh, answer can't be D...if u r thinking option A can be represented in form of P->Q, it can't actually....statement is in form of Q since P.....and "Q since P" and "if P then Q" are totally different.........