The next concept on our agenda is the Cartesian product of sets.

For sets \\(A\\) and \\(B\\), their (Cartesian) product \\(A \times B\\) is the set of all possible pairs (a,b), for a in A and b in B.

Example: suppose \\(A = \lbrace 1, 2 \rbrace\\) and \\(B = \lbrace 100, 200, 300 \rbrace \\).

Then \\(A \times B\\) = \\(\lbrace (1,100), (1,200), (1,300), (2,100), (2,200), (2,300) \rbrace\\).

This product has six elements.

The size of the product of A and B is the product of their sizes:

\\[|A \times B| = |A| \times |B|\\]