Existence quantifier

In mathematics and logic, the existence quantifier is a quantifier used to state that a proposition is true for at least one element in the universe of discourse. The existence quantifier is commonly written as $\exists$ (a mirrored E), and is read as "there exists". An example involving an existence quantifier is the statement "some natural number is equal to 3+5", which can be written as $\exists x\in \mathbb {N} ,\,x=3+5$.

In general, a statement of the form $\exists x\,P(x)$ is true if there is an x in the universe of discourse satisfying the predicate $P$, and is false otherwise. An existence quantifier is different from a universal quantifier, which is used to state that a proposition is true for all elements in the universe of discourse.

Related pages

• Predicate logic