Asymmetric relation


Definition 1

Let \((S, \mathcal{R})\) be a relational structure. Then \(\mathcal{R}\) is an asymmetric relation on \(S\) if and only if:

$$\forall x,y \in S : x{\mathcal{R}}y \Rightarrow \neg (y{\mathcal{R}}x)$$

Definition 2

ProofWiki

Proper supersets