Transitive Relation/Examples/Is an Ancestor of
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Example of Transitive 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 { $x$ is an ancestor of $y$}$
Then $\sim$ is a transitive relation.
Sources
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{I}$: Sets and Functions: Relations
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $1$: Sets and mappings: $\S 1.4$: Equivalence relations