# Anti-Reflexive Relation

## Anti-Reflexive Relation

Relation in a set E so that no element of E is related to itself.

In the representation of an anti-reflexive relation, there are no loops.

### Examples

• The relation “…is less than…” in the set of whole numbers is an anti-reflexive relation.
If 6 < 7, then 7 cannot be less than 6.
• The relation “…is the son of…” in a set of people is an anti-reflexive relation.
If Paul is Luke’s son, then Luke cannot be Paul’s son.