# Equivalence Class/Examples/People Born in Same Year

## 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 { $x$ and $y$ were born in the same year}$

Then the elements of the equivalence class of $x \in P$ is:

- $\eqclass x \sim = \set {\text {All people born in the same year as $x$} }$

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): Appendix $\text{A}.3$: Equivalence Relations: Problem Set $\text{A}.3$: $13$