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