Symmetric Relation/Examples/Is of Opposite Gender
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Example of Symmetric 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 { $x$ of the opposite gender to $y$}$
(This assumes that gender is binary and well-defined.)
Then $\sim$ is a symmetric relation.
However, $\sim$ is antireflexive and antitransitive.
Sources
- 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $1$: Pairs, Relations, and Functions: Exercise $9$