Quantifier

Definition

A quantifier is a logical operator that specifies the quantity of specimens in the domain of discourse that satisfy an open formula. The two most common quantifiers are the universal quantifier and the existential quantifier.

5 Must Know Facts For Your Next Test

1. The universal quantifier is symbolized by ∀ and means 'for all' or 'every'.
2. The existential quantifier is symbolized by ∃ and means 'there exists' or 'for some'.
3. Quantifiers can be used to form statements from predicates.
4. Negating a universally quantified statement results in an existentially quantified statement with a negated predicate, and vice versa.
5. In formal logic, scope of a quantifier refers to the part of a formula where the quantifier applies.

Review Questions

• What does the symbol ∀ represent?
• How would you negate an existentially quantified statement?
• What is the difference between a universal and an existential quantifier?

Related terms

Predicate: A function that returns true or false depending on its arguments.

LogicalOperator: A symbol or word used to connect two or more expressions.

DomainOfDiscourse: The set of all possible values that variables in logical statements can take.