In mathematics, the reflexive closure of a binary relation on a set is the smallest reflexive relation on that contains A relation is called reflexive if it relates every element of to itself.
For example, if is a set of distinct numbers and means " is less than ", then the reflexive closure of is the relation " is less than or equal to ".
The reflexive closure of a relation on a set is given by
In plain English, the reflexive closure of is the union of with the identity relation on
As an example, if
However, if any of the pairs in was absent, it would be inserted for the reflexive closure. For example, if on the same set