Inverse relation


Definition

ProofWiki
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

Proper supersets