What Is a Relation in Math?

In math, a relation describes how elements from one set, A, are related to elements of a second set, B, in terms of ordered pairs (x,y). For example, in a set of ordered pairs, the x-values can be the elements from set A and make up the domain. The y-values can be the elements from set B and form the range.

When finding the range for sets of ordered pairs, only the elements utilized in the relation make up the range. An example of this is using the following information: set A (x-values) contains the points (2, 4 and 3), set B has (y-values) with points (1, 6, 7, 8, 9 and 5) and the relation given is the set of ordered pairs (2,6), (4,6) and (3,7). In this example, the domain is (2, 4 and 3), the x-values of the ordered pairs of the given relation, while the range is (6 and 7), or the y-values. It is evident that not all the points contained in set B were used.