# 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:

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