A relation *from* set * to* set is a subset of their Cartesian product, . A relation between two sets is also called a *binary relation*. Relations between more than two sets are called *n-ary relations*.

More formally, a binary relation is defined as an ordered triple: . is the *domain* of the relation, is the *codomain*, and is the subset of , also known as the relation’s *graph*.

Since by definition is a set of ordered pairs , then for all ordered pairs where and , one, and only one of the following must be true:

- ; this is read “a is R-related to b” and is written .
- ; this is read “a is not R-related to b” and is written .

Some properties of binary relations:

- reflexive