# Equivalence Class/Examples/People of Same Age

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## 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}$

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

- $\eqclass x \sim = \set {\text {All people the same age as $x$ on their last birthday} }$

## Sources

- 1965: J.A. Green:
*Sets and Groups*... (previous) ... (next): $\S 2.4$. Equivalence classes