Suppose A and B be the two non-empty sets. The relation from the A to the B, i.e., the subset of A × B, is called a function (or a mapping) from A to B, when
(i) for each a ∈ A there exists b ∈ B such that (a, b) ∈ f
(ii) (a, b) ∈ f and (a, c) ∈ f ⇒ b = c
