Set product

Given two sets $A$ and $B$, we define the set product of $A$ and $B$, represented by $A\times B$, as the set $$A\times B=\{(x,y) \ | \ x\in A \ and \ y\in B \}$$

For example, $A = \{1,2,3\}$ and $B = \{a,b\}$, then $A \times B = \{(1,a), (1,b), (2,a), (2,b), (3,a) and (3,b)\}$.