GATE | GATE-CS-2017 (Set 2) | Question 11

Let p, q, r denote the statement “It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold” is represented by:
(A) (¬ p ∧ r) ∧ ((¬ r → (p ∧ q))
(B) (¬ p ∧ r) ∧ ((p ∧ q) → ¬ r)

(C) (¬ p ∧ r) ∨ ((p ∧ q) → ¬ r)
(D) (¬ p ∧ r) ∨ ((r → (p ∧ q))


Answer: (A)

Explanation: It is not raining (~p) and it is pleasent (r) : (¬p ∧ r)
It is raining (p) and it is cold (q) : (p∧q)
it is not pleasant (¬r) only if it is raining and it is cold : ¬r → (p∧q)
So the answer should be- (¬ p ∧ r) ∧ ((¬ r → (p ∧ q))

So, option (A) is true.

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