Equivalence Relation/Examples/People with Same Parents

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 { both of the parents of $x$ and $y$ are the same}$

Then $\sim$ is an equivalence relation.

Sources

• 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $1$: Sets and mappings: $\S 1.4$: Equivalence relations