Properties

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 "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[latex]^{2}[/latex] 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.

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