GATE 2013 CS (CS1) – Question 37

Engineering Mathematics · Discrete Mathematics: Propositional and First Order Logic · 2 marks · Multiple choice

With F(x)=“x is my friend” and P(x)=“x is perfect”, translate “None of my friends are perfect”.

$\exists x(F(x)\land\neg P(x))$
$\exists x(\neg F(x)\land P(x))$
$\exists x(\neg F(x)\land\neg P(x))$
$\neg\exists x(F(x)\land P(x))$

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Show answer and explanation

Correct answer: (D) $\neg\exists x(F(x)\land P(x))$

Explanation

The statement denies the existence of anyone who is simultaneously a friend and perfect: ¬∃x(F(x)∧P(x)), D. This is equivalent to ∀x(F(x)→¬P(x)); merely finding one imperfect friend would not suffice.

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