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A relation can be both symmetric and antisymmetric (in this case, it must be coreflexive), and there are relations which are neither symmetric nor antisymmetric (for example, the "preys on" relation on biological species). Antisymmetry is different from asymmetry: a relation is asymmetric if and only if it is antisymmetric and irreflexive.
Symmetric and antisymmetric relations. By definition, a nonempty relation cannot be both symmetric and asymmetric (where if a is related to b, then b cannot be related to a (in the same way)). However, a relation can be neither symmetric nor asymmetric, which is the case for "is less than or equal to" and "preys on").
Retrieved from "https://en.wikipedia.org/w/index.php?title=Anti-symmetric_relation&oldid=355612301"
A relation is connex if and only if its complement is asymmetric. A non-example is the "less than or equal" relation ≤ {\displaystyle \leq } . This is not asymmetric, because reversing for example, x ≤ x {\displaystyle x\leq x} produces x ≤ x {\displaystyle x\leq x} and both are true.
Relational sociology is a collection of sociological theories that emphasize relationalism over substantivalism in explanations and interpretations of social phenomena and is most directly connected to the work of Harrison White and Charles Tilly in the United States and Pierpaolo Donati and Nick Crossley in Europe.
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