# Equivalence Relation/Examples/People of Same Age

## Example of Equivalence Relation

Let $P$ be the set of people.

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

$\forall \tuple {x, y} \in P \times P: x \sim y \iff \text { the age of$x$and$y$on their last birthdays was the same}$

That is, that $x$ and $y$ are the same age.

Then $\sim$ is an equivalence relation.