Equivalence Relation/Examples/Non-Equivalence/People with Common Ancestor

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 $y$ have an ancestor in common}$

Then $\sim$ is an equivalence relation.