Inverse Relation Properties

Theorem
Let $\mathcal R$ be a relation on a set $S$.

If $\mathcal R$ has any of the properties:


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

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