# Cartesian Product of Sets

## Cartesian Product of Sets

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 “AB” is read as: “A Cartesian product B”.

• The Cartesian product is not commutative.
• The Cartesian product is also defined by: AB = {(x, y) | x ∈ A ∧ yB}.
• The Cartesian product AA 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 mn elements.