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} }$