Exercise 267Logic, sets and proofs › Quantifiers and negationHigh schoolAdded 3 Nov 2026

The existential quantifier

#existential quantifier#exists#example

Statement

Write in formal notation: "There exists an integer $n$ such that $n^2=4$ ." Determine its truth value.

Hint

Use $\exists$ for "there exists".

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Formal notation. $\exists n\in\mathbb{Z},\ n^2=4$ .

Truth value. True: $n=2$ (or $n=-2$ ) satisfies $n^2=4$ .

Conclusion. The statement is true.