Produsul cartezian a două mulțimi

Produsul cartezian al mulțimilor A și B este:

$A\times B=\left\{\left(x,y\right)\overline{)} x\in A, y\in B\right\}$

Observație: 

$A\times B\ne B\times A$

Exemplu:

$$\begin{gathered} A=\left\{1,2\right\} \\ B=\left\{3,4,5\right\} \\ A\times B=\left\{\left(1,3\right); \left(1,4\right); \left(1,5\right); \left(2,3\right); \left(2,4\right); \left(2,5\right)\right\} \\ B\times A=\left\{\left(3,1\right); \left(3,2\right); \left(4,1\right); \left(4,2\right); \left(5,1\right); \left(5,2\right)\right\} \\ A\times B\ne B\times A \\ A\times A=\left\{\left(1,1\right); \left(1,2\right); \left(2,1\right); \left(2,2\right)\right\} \end{gathered}$$