Quantifier

There are two quantifiers.

• The existential quantifier
• The universal quantifier

Existential Quantifier

The existential quantifier, $\exists$ is employed in formal logic to mean that something exists. Example of a true existential statement: $((S,\cdot )$ is a monoid) $⟹(\exists e\in S|e^2=e)$ $\forall x\in (\mathbb{Z},+)⟹\exists x^{-1}=-x$

Universal Quantifier

The universal quantifier, $\forall$, is employed in formal logic to mean that the statement following will apply to all examples of a given case. An example of a true universal statement in basic mathematics is: $\forall a,b\in \mathbb{Z},a+b=b+a$ This statement is also a Law.