Non-Reflexive Relation/Examples
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Examples of Non-Reflexive Relations
Arbitrary Non-Reflexive Relation 1
Let $V_1 = \set {y, z}$.
Let $S$ be the relation on $V_1$ defined as:
- $S = \set {\tuple {y, y}, \tuple {y, z} }$
Then $S$ is neither:
- a reflexive relation, as $\tuple {z, z} \notin S$
nor:
- an antireflexive relation, as $\tuple {y, y} \in S$
Thus $S$ is a non-reflexive relation.
Arbitrary Non-Reflexive Relation 2
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.