Exercise · ZW-EXISTENTIAL-QUANTIFIER-010 · ★★★ Advanced
Let D be empty. What is the value of ¬∃x P(x) in D?
Choose one option.
Show answer
- A. True
Explanation
In an empty domain there is no \(x\) to serve as a witness, so \(\exists x\,P(x)\) is false. Its negation \(\neg\exists x\,P(x)\) is therefore true.
Review the concept: Existential quantifier
Given a predicate \(P(x)\) over a domain \(D\), the existential quantifier asserts that \(P(x)\) is true for some \(x\in D\).
\[\exists x\,P(x)\]
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