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In logic, a quantifier is a language element that helps in generation of a quantification, which is a construct that mentions the number of specimens in the given domain of discourse satisfying a given open formula. Quantifiers are largely used in logic, natural languages and discrete mathematics.
Quantifiers are used in quantified expressions in which the free variables are bound by the quantifiers. In other words, the variables of the predicates are quantified by quantifiers. There are two well-known quantifiers used in predicate logic: the universal quantifier and the existential quantifier. The universal quantifier claims that statements within its scope are true for every value of the unique variable, whereas in the case of the existential quantifier, it claims that the statements within its scope are true only for some values of the specific variable. The universal quantifier is denoted by the symbol ∀, which is like an inverted A. The existential quantifier is denoted by the symbol ∃, which is like a backwards E.
Quantifier rank specifies the maximum depth of nesting possible for quantifiers inside a given formula. It has to be noted that the order of the quantifiers is crucial to the meaning of the logic. Quantifiers have wide usage in predicate logic and in discrete mathematics, as they help in translation of a given logical statement.