what is a relation

In mathematics, a relation is a way of describing a relationship between two sets of values. Specifically, a relation is a collection of ordered pairs containing one object from each set. For example, if we have two sets A and B, a relation between them could be {(a, b), (c, d)}, which means that a is related to b and c is related to d. A function is a type of relation, but a relation is allowed to have the object x in the first set to be related to more than one object in the second set. Relations can be reflexive, symmetric, transitive, or equivalence relations. To determine if a relation is a function, we can set up the relation as a table of ordered pairs and test to see if each element in the domain is matched with exactly one element in the range.