Symmetric Relation/Examples/Is a Brother of
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Example of Symmetric Relation
Let $P$ be the set of male 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 a brother of $y$}$
Then $\sim$ is a symmetric relation.
This does not hold if $P$ is the set of all people.
Because if $a$ is male and $b$ are brother and sister, then:
- $a \sim b$
but:
- $b \not \sim a$
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