Exercise 559Logic, sets and proofs › Quantifiers and negationHigh schoolAdded 3 Nov 2026

Quantifier over a finite set

#finite quantifier#exists#disjunction

Statement

Express $\exists x\in\{1,2,3\},\ P(x)$ without the existential quantifier.

Hint

Expand as a disjunction.

Show solutionHide solution

Expansion. $P(1)\lor P(2)\lor P(3)$ .

Conclusion. Existential over a finite set is a finite disjunction.

Dual. $\forall x\in\{1,2,3\},\ P(x)$ is $P(1)\land P(2)\land P(3)$ .