The Cartesian product of set

*A*by set*B*is the set of all ordered pairs for which the origin is an element of set*A*and the endpoint is an element in set*B*.### Symbol

The symbolism “*A* ☓ *B*” is read as: “A Cartesian product B”.

- The Cartesian product is not commutative.
- The Cartesian product is also defined by:
*A*☓*B*= {(*x*,*y*) |*x*∈*A*∧*y*∈*B*}. - The Cartesian product
*A*☓*A*is generally noted as*A*\(^{2}\) and is called the Cartesian square of*A*.

### Example

Consider the sets A = {*a*, *b*, *c*} and B = {0, 1, 2}.

Therefore: A ☓ B = {(*a*, 0), (*a*, 1), (*a*, 2), (*b*, 0), (*b*, 1), (*b*, 2), (*c*, 0), (*c*, 1), (*c*, 2)}.

If set A includes *m* elements and set B includes *n* elements, then the Cartesian product A ☓ B includes *m* ☓ *n* elements.