# Symmetric Relation/Examples

## Examples of Symmetric Relations

### Brotherhood Relation

Let $P$ be the set of male people.

Let $\sim$ be the relation on $P$ defined as:

$\forall \tuple {x, y} \in P \times P: x \sim y \iff \text {$x$is a brother of$y$}$

Then $\sim$ is a symmetric relation.

This does not hold if $P$ is the set of all people.

Because if $a$ is male and $b$ are brother and sister, then:

$a \sim b$

but:

$b \not \sim a$