# Cartesian product

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The Cartesian product of two sets $A,B$ , denoted by $A\times B$ , is the set of all possible ordered pairs whose first component is an element of $A$ and whose second component is an element of $B$ .

Definition

Given two sets $A,B$ ,
$A\times B=\{(x,y)|x\in A\and y\in B\}$

## Example

Suppose $A=\{0,1\}$ and $B=\{a,c\}$ :

$A\times B=\{(0,a),(0,c),(1,a),(1,c)\}$