Non-Reflexive Relation/Examples/Arbitrary Non-Reflexive Relation 1

Example of Non-Reflexive Relation

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.

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.2$: Cartesian Products and Relations