Question 8038 – GATE 2016 [Set-1]

Let p,q,r,s represent the following propositions.
p: x ∈ {8,9,10,11,12}
q: x is a composite number
r: x is a perfect square<
s: x is a prime number
The integer x≥2 which satisfies ¬((p ⇒ q) ∧ (¬r ∨ ¬s))  is _________.

Correct Answer: A

Question 11 Explanation: 
Given,
~((p→q) ∧ (~r ∨ ~S))
⇒ first simplify the given statement by converging them to ∧, ∨
⇒ [~(p→q) ∨ (~(~r ∨ ~s)]
Demorgan’s law:
⇒ [~(~p ∨ q) ∨ (r ∧ s)]

∵ p→q ≡ ~p ∨ q

⇒ [(p ∧ ~q) ∨ (r ∧ s)]
p ∧ ~q is {8,9,10,11,12} ∧ {not a composite number} i.e. {11}
r ∧ s is {perfect square} ∧ {prime} i.e. no answer
So, the one and only answer is 11.
A
11
B
12
C
13
D
14
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