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