Non-reflexive Relation/Examples/Arbitrary Non-reflexive Relation 2

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Example of Non-reflexive Relation

Let $S = \set {a, b}$.

Let $\mathcal R$ be the relation on $S$ defined as:

$\mathcal R = \set {\paren {a, a} }$

Then $\mathcal R$ is neither:

a reflexive relation, as $\tuple {b, b} \notin \mathcal R$

nor:

an antireflexive relation, as $\tuple {a, a} \in \mathcal R$

Thus $\mathcal R$ is a non-reflexive relation.