Exercise · ZW-UNIVERSAL-QUANTIFIER-010 · ★★★ Advanced
In an empty domain, ∀x P(x) is considered...
Choose one option.
Show answer
- C. Vacuously true
Explanation
With no elements there is no counterexample, so \(\forall x\,P(x)\) is vacuously true.
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-008 To refute ∀x P(x) it is enough to find...