Exercise · ZW-UNIVERSAL-QUANTIFIER-009 · ★★★ Advanced
Which statement is equivalent to \(\forall x\,P(x)\)?
Choose one option.
Show answer
- D. Every element satisfies P
Explanation
"Every element satisfies P" is equivalent to \(\forall x\,P(x)\); the others talk about some x or the negation of the universal.
Review the concept: Universal quantifier
Given a predicate \(P(x)\) over a domain \(D\), the universal quantifier asserts that \(P(x)\) is true for every \(x\in D\).
\[\forall x\,P(x)\]
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