Predicate Logic

Property: predicate that asserts a certain property.

Predicate P meaning "is-even" and ranging over the integers: ∀x ∈ ℤ. (x ÷ 2 = 0) -> E(x)

is, actually, a biconditional (iff) because the inverse also holds: ∀x ∈ ℤ. (x ÷ 2 = 0) <-> E(x)

also, the first part, ∀x ∈ ℤ, is a shorthand for ∀x. x ∈ ℤ

• shorthand ∀x ∈ S. P(x), expanded ∀x. x ∈ S -> P(x)

• shorthand ∃x ∈ S. P(x), expanded ∀x. x ∈ S ∧ P(x)