# Cartesian product

set of the ordered pairs such that the first element of the pair is in the first element of the product and the second element of the pair is in the second element of the product

In mathematics, sets can be used to make new sets. Suppose we have two sets A and B. Then the Cartesian product of A with B is written as A × B and is the set of all ordered pairs whose first element is a member of A and whose second element is a member of B.

For example, let A = {1, 2, 3} and B = {a, b}. Then:

${\displaystyle A\times B=\{(1,a),(1,b),(2,a),(2,b),(3,a),(3,b)\}}$