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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?

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

### 1 comment

Why not (B) ?

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"

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 ?

I also have same doubt.
P since Q ≡ (¬Q⟹¬P)

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

So  (¬Q⟹¬P)  ≡ P->Q
Very good explanation

@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.........