Equivalence Relation/Examples/People with Same First Name
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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 { $x$ and $y$ have the same first name}$
Then $\sim$ is an equivalence relation.
Sources
- 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.3$: Equivalence Relations: $(5)$