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.