Relations: Overview

Relations on sets

Ordered pair

Cartesian product

A Cartesian product is a mathematical operation on sets that returns a new set, called the product set (or simply product).

That is, for sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B.

Products can be specified using set-builder notation:

{\displaystyle A\times B={\,(a,b)\mid a\in A {\mbox{ and }} b\in B\,}.}A\times B={\,(a,b)\mid a\in A {\mbox{ and }} b\in B\,}.