Exercise · ZW-EXISTENTIAL-QUANTIFIER-007 · ★★☆ Intermediate
∃x P(x) is true when...
Choose one option.
Show answer
- D. There is at least one x that satisfies P
Explanation
\(\exists x\,P(x)\) is true when there is at least one \(x\) in the domain satisfying \(P\). A single witness is enough.
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-008 To prove ∃x P(x), it is usually enough to exhibit...
- ZW-EXISTENTIAL-QUANTIFIER-009 Select expressions that imply there is at least one object.
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