Exercise 1157Logic, sets and proofs › Quantifiers and negationL1Added 3 Nov 2026

Free and bound variables

#free variable#bound variable#quantifier

Statement

In $\forall x,\ (P(x)\land Q(y))$ , identify free and bound variables.

Hint

Variables under the scope of a quantifier are bound; others are free.

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Bound. $x$ is bound by $\forall x$ .

Free. $y$ is free (not quantified).

Closure. If we add $\exists y$ at the front, then $y$ becomes bound too.

Conclusion. Free variables affect the truth value given an assignment; bound variables are internal.