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.


Answer: (D)

Explanation: P = I study hard.
Q = I qualify the GATE.
R = I get admission in IIT.
Let’s Solve
S1: (¬P → ¬Q )
S2: (R → Q)
Contradiction S2: (¬Q → ¬R)
Then we get (¬P → Q) ∧ (¬Q → ¬R) ≡ (¬P → ¬R)

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


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