Quantifier

logic

Universal

Definition

Universal Quantifier

The universal quantifier, denoted by the symbol $\forall$, is a quantifier used in logic to express that a property or predicate holds for all elements in the domain of discourse.

A formula $\forall xF$ is true if and only if $F$ is true for every possible value assigned to $x$ from the universe.

Link to original

Existenial

Definition

Existential Quantifier

The existential quantifier, denoted by the symbol $\exists$, is a quantifier used in logic to express that there exists at least one element in the domain of discourse that satisfies a given predicate.

A formula $\exists xF$ is true if and only if there is some value in the universe that, when assigned to $x$, makes $F$ true.

Link to original