Inverse Relation Properties

Theorem
Let $\RR$ be a relation on a set $S$.

If $\RR$ has any of the properties:


 * Reflexive
 * Antireflexive
 * Non-reflexive
 * Symmetric
 * Asymmetric
 * Antisymmetric
 * Non-symmetric
 * Transitive
 * Antitransitive
 * Non-transitive

then its inverse $\RR^{-1}$ has the same properties.