Cartesian Product of Crisp Sets A and B

The Cartesian product of two sets A & B is denoted by A X B and is the set of all ordered pairs such that the first element in the pair belongs to set A and second element belong to set B.

It can be observed that cardinality of A X B is the product of cardinality of individual sets.

A = { 1, 2, 3 }

B = { a, b }

A X B = { (1, a), (1, b), (2, a), (2, b), (3, a), (3, b) }

Other Crisp Relations :-

Any crisp relation R (x1, x2, x3………….xn) among crisp sets x1, x2, x3,…………….,xn is a subset of the Cartesian product.

• for n = 2 the relation R(x1, x2) is called binary relation.
• for n = 3 the relation R(x1, x2, x3) is called ternary relation.
• for n = 4 the relation R(x1, x2, x3, x4) is called quaternary relation.
• for n = 5 the relation R(x1, x2, x3, x4, x5) is called quinary relation.