You have seen different types of relations in the previous section. A relation which is not one-to-many is a function. That is, a function is a special type of relation where no element of its domain is paired with more than one element of its range. Thus, function is defined as follows.

Definition

A function f from A to B is a relation from A to B in which each element of A is related (paired) to only one of the elements of B.

That is, for every x∈A there is only one y∈B such that (x, y) ∈ f.

So, a relation fails to bet a function if it has two ordered pairs (x, y) and (x, z) such that y ≠ z.

Example

Consider the relation R = {(1, 2), (7, 8), (4, 3), (7, 6)}
R is not a function because (7, 8) and (7, 6) are in R but 8 ≠ 6,