Definition:Non-Symmetric Relation

Definition
Let $\RR \subseteq S \times S$ be a relation in $S$. $\RR$ is non-symmetric it is neither symmetric nor asymmetric.

Example
An example of a non-symmetric relation:

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


 * $\RR$ is not symmetric, because $\tuple {a, c} \in \RR$ but $\tuple {c, a} \notin \RR$.


 * $\RR$ is not asymmetric, because $\tuple {a, b} \in \RR$ and $\tuple {b, a} \in \RR$ also.

Also see

 * Definition:Symmetry (Relation)


 * Definition:Symmetric Relation
 * Definition:Asymmetric Relation
 * Definition:Antisymmetric Relation