# Definition:Non-transitive Relation

(Redirected from Definition:Non-Transitive Relation)

## Contents

## Definition

Let $\mathcal R \subseteq S \times S$ be a relation in $S$.

$\mathcal R$ is **non-transitive** if and only if it is neither transitive nor antitransitive.

## Also known as

Some sources use the term **intransitive**.

However, as **intransitive** is also found in other sources to mean antitransitive, it is better to use the clumsier, but less ambiguous, **non-transitive**.

## Also see

- Results about
**relation transitivity**can be found here.

## Sources

- 1965: E.J. Lemmon:
*Beginning Logic*... (previous) ... (next): $\S 4.5$: Properties of Relations