What is Irreflexive Relation?

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

(a, a) ∉ R ∀ 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 not be present in the relation R. If any such aRa is present in R then R is not an irreflexive relation.

Example:

Consider set A = {a, b}.

Then R = { (a, a), (a, b) } is not irreflexive relation.
and R₁ = { (a, b), (b, a) } is a irreflexive relation

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“.