Let A and B be two sets. Then a relation R from A to B is a subset of A×B.
R is a relation from A to B <=> R is a subset of A×B.
Total number of relations: If A and B are two non empty sets with m and n elements respectively, A×B consists of mn ordered pairs.
Since each subset defines a relation from A to B, so total number of relations from A to B is 2mn.