Overview of Existential and Universal Quantification

A detailed tutoral on existential and universal quantification. Step by step tutorial including several examples of existential and universal quantification for reference.

Existential and universal quantifiers give us different ways to write expressions and mathematical equations. The existential quanitfier looks like a backwards capital E, and basically means “some”. The universal quantifier looks like an upside down A, and basically means “all”. For example, take the sentence “Some children don’t like clowns.” In the mathematical form of quantifiers, this would be written as (Ex) (x is a child) ^ (Ay) (y is a clown) –> (x does not like y). “Some children” indicates that you would use an existential quantifier, not a universal quantifier. Since clowns in not specific, based on context we must assume that the statement refers to all clown, and therefore we use the universal quantifier. The ^ is the symbol for “and”, implying that both of these statements are true, and the arrow is an implication stating that if there is a clown, some children will not like it based on the previous statement.