Project ForgeWhat is the logical translation of the following statement, where F(x) means 'x is a friend' and P(x) means 'x is perfect'?
"None of my friends are perfect."
- A∃x(F(x) ∧ ¬P(x))
- B∃x(¬F(x) ∧ P(x))
- C∃x(¬F(x) ∧ ¬P(x))
- ¬∃x(F(x) ∧ P(x))
Explanation
The Symbol-font quantifier/negation glyphs render as blanks in the source PDF for this question, but the option structure is unambiguous: options A, B, C all assert ∃x(...) — 'there EXISTS someone with some property' — which can never correctly express a universal 'NONE are' claim. Only option D has the needed outer negated-existential structure ¬∃x(F(x)∧P(x)) — 'there does NOT exist a friend who is perfect' — which is exactly the meaning of 'none of my friends are perfect.'
Source: GATE CS 2013 (2013)
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