Exercise · ZW-EXISTENTIAL-QUANTIFIER-009 · ★★☆ Intermediate
Select expressions that imply there is at least one object.
Choose one option.
Show answer
- B. \(\exists x\,P(x)\)
Explanation
\(\exists x\,P(x)\) directly asserts that some object has \(P\). The others do not guarantee that any object exists: \(\neg\exists x\,P(x)\) asserts the opposite, and \(\forall x\,\neg P(x)\) is vacuously true on an empty domain.
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 \(x\in D\).
\[\exists x\,P(x)\]
More practice problems: existential quantifier
- ZW-EXISTENTIAL-QUANTIFIER-001 The symbol of the existential quantifier is...
- ZW-EXISTENTIAL-QUANTIFIER-002 ∃x P(x) means that P(x) holds...
- ZW-EXISTENTIAL-QUANTIFIER-003 To prove an existential statement it is enough to provide...
- ZW-EXISTENTIAL-QUANTIFIER-004 Which statement is existential?
- ZW-EXISTENTIAL-QUANTIFIER-005 If there is at least one x in the domain with P(x) true, ∃x P(x) is...
- ZW-EXISTENTIAL-QUANTIFIER-006 The symbol ∃ is read...
- ZW-EXISTENTIAL-QUANTIFIER-007 ∃x P(x) is true when...
- ZW-EXISTENTIAL-QUANTIFIER-008 To prove ∃x P(x), it is usually enough to exhibit...
← ZW-EXISTENTIAL-QUANTIFIER-008 ZW-EXISTENTIAL-QUANTIFIER-010 →