Equivalence Relation/Examples/People of Same Age

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}$

That is, that $x$ and $y$ are the same age.

Then $\sim$ is an equivalence relation.

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 2.2$. Equivalence relations: Example $30$
• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 2.3$. Partitions: Example $34$
• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.2$: Cartesian Products and Relations: Example $\text{A}.2$