Binary Relations
Suppose S is a set. Let a ? S and b ? S.
Then (a, b) is an ordered pair of elements of S.
The set of all ordered pairs over S is:
{ (x, y) | x ? S, y ? S }
= the set of all ordered pairs (x, y) such that x is in S and y is in S.
Any set of ordered pairs over S is called a binary relation on S.