# Inverse relation

## Definition

THEOREM    $$\left(\mathrel{R}^{-1}\right)^{-1} = \mathrel{R}$$

Proof available

THEOREM

Let $$\mathrel{R}$$ be a relation on a set $$S$$. If $$\mathrel{R}$$ is reflexive, then so is (\mathrel{R^{-1}}\).

Proof available

THEOREM

Let $$\mathrel{R}$$ be a relation on a set $$S$$. If $$\mathrel{R}$$ is antisymmetric, then so is $$\mathrel{R^{-1}}$$.

Proof available