Relation defined in a set E so that all elements

*x*of E are related to themselves.- The arrow diagram of a reflexive relation in a set E includes loops in each of its points.
- A relation in a set E that does not contain any loops is called
**anti-reflexive**while a relation in E that is neither reflexive nor anti-reflexive is called**non-reflexive**.

### Examples

- In the set \(\mathbb {N}\) of whole numbers, the relation “…
*divides*…” is a**non-reflexive relation**. In its arrow diagram, we find loops in all of its points except 0, because 0 cannot be divided by itself. - In the set \(\mathbb {N}^{\ast}\) of non-zero whole numbers, the relation “…divides…” is a
**reflexive relation**. - In the set \(\mathbb {N}^{\ast}\) of non-zero whole numbers, the relation “…is relatively prime with…” is an
**anti-reflexive relation**.