Equivalence Class/Examples/People with Same Height

Example of Equivalence Relation

Let $A = \set {u, v, w, x, y, z}$ be a set of people.

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

$\forall \tuple {a, b} \in A \times A: x \sim y \iff \text { $a$ and $b$ are the same height}$

Let:

$u, v, w$ be the same height

$x, y, z$ be the same height but different from the height of $u, v, w$.

Then the equivalence class of $x \in A$ are $\set {u, v, w}$ and $\set {x, y, z}$.