Transitive Relation/Examples

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Examples of Transitive Relations

Ancestor 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.

Less Than on Real Numbers

Let $<$ be the usual ordering on the set of real numbers $\R$.

Then $<$ is a transitive relation, but neither reflexive nor symmetric.