Given sets A and B, any subset of is a relation between A and B. If this is often denoted by
If , is said to be a relation on
The domain of a relation between and is the set
The range of a relation between and is the set
Let be a relation between and .
The inverse of the relation dentoed by
is a relation between and , defined by
Let be a relation between and , and let be a relation between and .
The composition of and , denoted by , is a relation between and defined by
A relation on is reflexive if for all .
A relation on is symmetric if for all .
A relation on is antisymmetric if .
A relation is transitive if whenever , then