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Discrete Mathematics

GATE CSE 2013 · Q27

MCQ2 marksEasy

Time

What is the logical translation of the following statement? “None of my friends are perfect.”

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Official answer: D) eg ∃ x(F(x) ∧ P(x))

Discrete Mathematics

Let F(x)F(x) denote "xx is my friend" and P(x)P(x) denote "xx is perfect".

The statement "None of my friends are perfect" means "There is no person who is both my friend and perfect."

In first-order logic, this is directly translated as: eg∃x(F(x)∧P(x)) eg \exists x (F(x) \land P(x))

Equivalently, it can be written as $\forall x (F(x) \rightarroweg P(x))$.

Thus, (D) is the correct translation.

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This Discrete Mathematics previous year question is Q27 of the GATE CSE 2013 paper. Find more GATE CSE PYQs on Discrete Mathematics in Engineering Mathematics, or browse all GATE CSE PYQs.

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Discrete Mathematics in GATE CSE

Discrete Mathematics has 50 GATE CSE PYQs across 23 papers from 2011 to 2026. 11 of them are 2-mark MCQs like this one, and GATE CSE 2013 has 4.

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GateAI solution cardGATE CSE 2013 · Q27 · MCQ

What is the logical translation of the following statement? “None of my friends are perfect.”

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.