Exercise 268Logic, sets and proofs › Quantifiers and negationHigh schoolAdded 3 Nov 2026

The universal quantifier

#universal quantifier#forall#proposition

Statement

Write in formal notation: "For every real number $x$ , $x^2\ge0$ ." Then determine whether the statement is true or false.

Hint

Use $\forall$ for "for every" and $\in\mathbb{R}$ for the domain.

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Formal notation. $\forall x\in\mathbb{R},\ x^2\ge0$ .

Truth value. True: for any real number, its square is nonnegative.

Conclusion. The statement is true.