Cartesian Product of Two Sets

The Cartesian product is the bridge that turns two separate sets into a single set of ordered pairs, where the first element always comes from the first set and the second from the second. If you have a set $A$ of shirts and a set $B$ of trousers, then $A \times B$ lists every possible outfit — each shirt paired with each trouser. This idea of pairing every element of one set with every element of ano …