Category:Connected Relations

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This category contains results about Connected Relations.

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

Then $\mathcal R$ is connected if and only if:

$\forall a, b \in S: a \ne b \implies \tuple {a, b} \in \mathcal R \lor \tuple {b, a} \in \mathcal R$

That is, if and only if every pair of distinct elements is related (either or both ways round).