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# AntiSymmetry

## Basic idea

A relation is antisymmetric if no two distinct elements are mutually related. Together with reflexivity and transitivity it defines a partial order.

## Key formulas

* $\forall a,b \in X.; (R(a,b) \land R(b,a)) \Rightarrow a = b$
* Equivalently: $R \cap R^{-1} \subseteq \Delta\_X$

In mathematics, a homogeneous relation **R** on set X is antisymmetric if there is no pair of distinct elements of X each of which is related by **R** to the other. More formally, **R** is antisymmetric precisely if for all a and b in X.

If R(a,b) holds then R(b,a) must not hold

or equivalently: if R(a,b) == R(b,a) then a==b