What is the logical translation of the following statement? “None of my friends are perfect.”
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GATE CSE 2013 · Q27
Time
Select one answerSingle correct
Solution
Official answer: D) eg ∃ x(F(x) ∧ P(x))
Discrete MathematicsLet denote " is my friend" and denote " 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:
Equivalently, it can be written as $\forall x (F(x) \rightarroweg P(x))$.
Thus, (D) is the correct translation.
Try the question first, then check your work.
Examiner trap
"None of A are B" means there does not exist any entity that is both A and B.
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 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.
How GATE tests Discrete MathematicsIndependent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.