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|\$