Suppose A and B be two non-empty sets then every subset of A Χ B describes a relation from A to B and each relation from A to B is subset of AΧB.

Consider R : AΧB and (a, b) € R. then we can declare that a is associated to b by the relation R and write it as

a R b. If (a, b) ¢R, we write it as a      b.

Example  Let A {1, 2, 3, 4, 5}, B = {1, 3}

               We set a relation from A to B as: a R b iff a ≤ b; a € A, b € B. Then

               R ={(1, 1), (1, 3), (2, 3), (3, 3)}AΧB