Definition 5.38.2 (Antisymmetric)

#Definition

A relation $R$ on a set $A$ such that for all $a, b \in A$ if $(a, b) \in R$ and $(b, a) \in R$ , then $a = b$ , is called $antisymmetric$

Tip

Antisymmetry can be formalised is predicate logic by

\forall x \forall y (((x, y) \in R \land (y, x) \in R) \to x = y)

Here, the domain is the set of all elements in $A$