What do you mean by the term cartesian product

The set of all ordered pairs <a, b>, where a is an element of A and b is an element of B, is called the Cartesian product of A and B and is denoted by A×B.

Example 1: Let A = {1, 2, 3} and B = {a, b}. Then A × B = {<1, a>, <1, b>, <2, a>, <2, b>, <3, a>, <3, b>}.

Example 2: For the same A and B as in Example 1,

B × A = {<a, 1>, <a, 2>, <a, 3>, <b, 1>, <b, 2>, <b, 3>}.

As you can see in these examples, in general, A ×B ≠B ×A unless A = ∅, B = ∅ or A = B.

Note that A × ∅= ∅ × A = ∅ because there is no element in ∅ to form ordered pairs with elements of A.

The concept of Cartesian product can be extended to that of more than two sets.