Non-Reflexive Relation/Examples/Arbitrary Non-Reflexive Relation 2

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.