Logical quantifier
English statements can be often rewritten using symbols, predicates representing criteria, and quantifiers. One example is "Each of Peter's friends either likes to dance or likes to go to the beach". Let X be the set of all Peter's friends. Let P(x) be the predicate "x likes to dance". Let Q(x) be the predicate "x likes to go to the beach". We can rewrite the example using formal notation as . The statement can be read as "For every x that is a member of X, P applies to x or Q applies to x."