Universal and Existential Quantifiers, ∀ “For All” and ∃ “There Exists”

Statements with “for all” and “there exist” in them are called quantified statements. “For all”, written with the symbol ∀, is called the Universal Quantifier and and “There Exists” , written with the symbol ∃, is called the Existential Quantifier. A quantifier turns a predicate such as “x is greater than 7” into a statement that can be true for false. For instance, “For all x, x is greater than 7” is false as 2 is not greater than 7, but “There Exists an x such that x is greater than 7” is true as 8 is greater than 7.

Learning Objectives
1) Be able to use the Universal and Existential quantifiers in a sentence
2) Observe that a Quantified Predicate is a Logical Statement

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