# GATE | Sudo GATE 2020 Mock II (10 January 2019) | Question 40

Consider the following two statements.

• S1: If I don’t study hard, I will not qualify in GATE.
• S2: If I get admission in IIT, I qualified in GATE.

Which one of the following statements follows from S1 and S2 as per sound inference rules of logic?
(A) If I qualified the GATE,I can not get admission in IIT.
(B) If I don’t study hard,I can get admission in IIT.
(C) If I qualify the GATE, I can get admission in IIT.
(D) If I don’t study hard,I can not get admission in IIT.

Explanation: Let,

```P = I study hard,
Q = I qualify the GATE,
R = I get admission in IIT ```

So,

```S1: (¬P → ¬Q )
S2: (R → Q) ```

Contradiction S2: (¬Q → ¬R), because contradiction of implication is also true. Now,

`(¬P → ¬Q) ∧ (¬Q → ¬R) ≡ (¬P → ¬R) `

Hence, “If I don’t study hard, I can not get admission in IIT”.

Option (D) is correct.

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