A relation is a function if it “maps” elements of one set to another set. That means that each element in the first set can appear at most in one pair in the first entry.The example shows two elements of the first set can be mapped to the same element of the second set.

A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product set A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.The set of all first elements in a relation R is called the domain of the relation B, and the set of all second elements called images is called the range of R.