# Anti-symmetric relation

## Definition

A binary relation $$\mathrel{R}$$, on a set $$S$$, is anti-symmetric if and only if:

$$\forall x,y \in S : x{\mathrel{R}}y \wedge y{\mathrel{R}}x \Rightarrow x = y$$
THEOREM

The less than or equal to relation is anti-symmetric.

Proof unavailable