A cartesian product between two sets is defined as the set consisting of all possible ordered pairs that can be formed by taking one element from each of the sets at a given time.

If A and B are two sets such that a ∈ A and b ∈ B, then the cartesian product between A and B is denoted as A × B and is evaluated as { (a,b) } where a ∈ A and b ∈ B.

Let A = { 1,2 } and B = { x,y }

The cartesian product of A and B denoted as A × B =

{ (1,x) , (1,y), (2,x), (2,y) }

The cartesian product of B and A, denoted as B × A =

{ (x,1) , (x,2), (y,1), (y,2) }

Clearly A × B ≠ B × A