Symmetric Relation

Symmetric Relation

## Definition / Concept

A relation $R$ on $A$ is symmetric if reversing every related ordered pair also gives a related ordered pair.

## Formula

$$aRb\Rightarrow bRa$$

$$(a,b)\in R\Rightarrow(b,a)\in R$$

## Conditions / Special Cases

For a set containing $n$ elements, the number of symmetric relations is:

$$2^{\frac{n(n+1)}{2}}$$

## Usage

- Used to test symmetry of a relation.

- Used in counting symmetric relations.