Exercise · ZW-UNIVERSAL-QUANTIFIER-003 · ★☆☆ Basic

To refute a universal statement it is enough to find...

Choose one option.

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  • B. A counterexample

Explanation

One element of the domain where \(P(x)\) is false refutes the universal statement: a counterexample.

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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

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