Reflexive Relation

Reflexive Relation

## Definition / Concept

A relation $R$ on $A$ is reflexive if every element of $A$ is related to itself.

## Formula

$$\forall a\in A,\quad(a,a)\in R$$

## Conditions / Special Cases

If:

$$n(A)=n$$

then all $n$ diagonal ordered pairs must belong to $R$.

The remaining:

$$n^2-n$$

ordered pairs are optional.

Therefore, the number of reflexive relations is:

$$2^{n^2-n}$$

## Usage

- Used to check whether a relation is reflexive.

- Used in counting reflexive relations.