Definition:Non-Symmetric Relation

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

Example
An example of a non-symmetric relation:

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


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


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

Also see

 * Definition:Symmetry (Relation)


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