Cartesian Product and Ordered Pairs — A Quick Recap

The previous chapter introduced the Cartesian product of two finite sets $A$ and $B$: the set $A \times B = \{(a,b) : a \in A, b \in B\}$ of all ordered pairs formed by taking one element from $A$ (first) and one from $B$ (second), with $n(A \times B) = n(A) \times n(B)$. This idea is recapped here because it is exactly what the rest of this chapter needs next: a function, as the next two sections define it, is nothing more than a specially-chosen subset of ordered pairs from $A \times B$ — one that follows a particular rule about how the pairs are chosen.

For example, if $A = \{1, 2, 3\}$ and $B = \{p, q\}$, then

$A \times B = \{(1,p), (1,q), (2,p), (2,q), (3,p), (3,q)\},$ …