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# Logical quantifiers

Logical quantifiers are used in first order logic and in logic of higher order.

## Existential quantifier

The existential quantifier, i.e. there exists at least one, is denoted with the inverted latin character ${\displaystyle \scriptstyle \exists \,}$.

## Uniqueness quantifier

The uniqueness quantifier, i.e. there exists one and only one, is denoted with ${\displaystyle \scriptstyle \exists !\,}$.

Example:

${\displaystyle \exists !\,p\in \mathbb {N} :p{\text{ prime and }}p{\text{ even}}.}$

## Universal quantifier

The universal quantifier, i.e. for all, is denoted with the inverted latin character ${\displaystyle \scriptstyle \forall \,}$.