the best-known quantifiers are the "existential quantifier", represented by ∃, and the "universal quantifier", represented by ∀. the existential quantifier is used to express statements of the form "there exists", and is true precisely when there is at least one mathematical object from the universe of discourse that matches the predicate or formula. on the other hand, the universal quantifier is used to express statements of the form "for all", and is true precisely when all possible mathematical objects of the universe of discourse match the specified predicate or formula.