GATE | GATE-CS-2016 (Set 1) | Question 11

Let p, q, r, s represent the following propositions.

p: {8, 9, 10, 11, 12}
q: x is a composite number
r: x is a perfect square
s: x is a prime number

Note : This question was asked as Numerical Answer Type.
(A) 8
(B) 9
(C) 11
(D) 12


Answer: (C)

Explanation: (p ⇒ q) will give {8, 9, 10, 12}
¬r will give {8, 10, 11, 12}
¬s will give {8, 9, 10, 12}
(¬r ∨ ¬s) will give {8, 9, 10, 11, 12}
(p ⇒ q) ∧ (¬r ∨ ¬s) will give {8, 9, 10, 12}
¬((p ⇒ q) ∧ (¬r ∨ ¬s)) will give 11.

Thus, C is the correct option.

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