Anti-Symmetric Relation

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math

A property of a relation \( R \subseteq A \times B \) where no pair of distinct elements of \( X = A \times B \) each of [see page 20, which] is related by \( R \) to the other.

\begin{align*} \forall a \in A, b \in B ((a R b) \implies a = b) \
\forall a \in A, b \in B ((a R b) \land (a \neq b) \implies \neg (b R a)) \end{align*}