Non-Reflexive Relation/Examples/Arbitrary Non-Reflexive Relation 2
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Example of Non-Reflexive Relation
Let $S = \set {a, b}$.
Let $\RR$ be the relation on $S$ defined as:
- $\RR = \set {\paren {a, a} }$
Then $\RR$ is neither:
- a reflexive relation, as $\tuple {b, b} \notin \RR$
nor:
- an antireflexive relation, as $\tuple {a, a} \in \RR$
Thus $\RR$ is a non-reflexive relation.