Exercise 560Logic, sets and proofs › Quantifiers and negationHigh schoolAdded 3 Nov 2026

Negating an existential statement

#negation#existential#exists

Statement

Negate the statement: $\exists x\in\mathbb{R},\ x^2=-1$ . Is the negation true?

Hint

$\neg(\exists x,\ P(x))\equiv\forall x,\ \neg P(x)$ .

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Negation. $\forall x\in\mathbb{R},\ x^2\neq-1$ .

Truth value. True: no real number squares to $-1$ .

Conclusion. The original statement is false; its negation is true.