What is a Reflexive Relation?

A relation R on a set A is called reflexive relation if 

(a, a) ∈ R ∀ a ∈ A, i.e. aRa for all a ∈ A, 
where R is a subset of (A x A), i.e. the cartesian product of set A with itself.

This means if element “a” is present in set A, then a relation “a” to “a” (aRa) should be present in relation R. If any such aRa is not present in R then R is not a reflexive relation.

A reflexive relation is denoted as:

I_A = {(a, a): a ∈ A}

Example:

Consider set A = {a, b} and R = {(a, a), (b, b)}.
Here R is a reflexive relation as for both a and b, aRa and bRb are present in the set.

A relation is a subset of the cartesian product of a set with another set. A relation contains ordered pairs of elements of the set it is defined on. To learn more about relations refer to the article on “Relation and their types“.