Exercise · ZW-UNIVERSAL-QUANTIFIER-008 · ★★☆ Intermediate
To refute ∀x P(x) it is enough to find...
Choose one option.
Show answer
- A. A counterexample
Explanation
A single case in the domain where \(P(x)\) fails is enough to refute \(\forall x\,P(x)\).
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 \(x\in D\).
\[\forall x\,P(x)\]
More practice problems: universal quantifier
- ZW-UNIVERSAL-QUANTIFIER-001 The symbol of the universal quantifier is...
- ZW-UNIVERSAL-QUANTIFIER-002 ∀x P(x) means that P(x) holds...
- ZW-UNIVERSAL-QUANTIFIER-003 To refute a universal statement it is enough to find...
- ZW-UNIVERSAL-QUANTIFIER-004 Which statement is universal?
- ZW-UNIVERSAL-QUANTIFIER-005 If P(x) is true for every x in the domain, ∀x P(x) is...
- ZW-UNIVERSAL-QUANTIFIER-006 The symbol ∀ is read...
- ZW-UNIVERSAL-QUANTIFIER-007 ∀x P(x) is true when...
- ZW-UNIVERSAL-QUANTIFIER-009 Which statement is equivalent to ∀ x P(x)?