is the only relation that is (vacuously) both symmetric and asymmetric.

Properties

The following conditions are sufficient for a relation to be asymmetric:
* is irreflexive and anti-symmetric (this is also necessary)
* is irreflexive and transitive. A transitive relation is asymmetric if and only if it is irreflexive: if and transitivity gives contradicting irreflexivity. Such a relation is a strict partial order.

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