Exercise 270Logic, sets and proofs › Quantifiers and negationHigh schoolAdded 3 Nov 2026

Proving an existential statement

#existential proof#example#witness

Statement

Prove: $\exists n\in\mathbb{N},\ n^2-n=6$ .

Hint

Find a witness $n$ and verify.

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Witness. $n=3$ satisfies $n^2-n=9-3=6$ .

Conclusion. The existential statement is true with witness $n=3$ .