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: if whenever are such that then necessarily A relation is coreflexive if and only if its symmetric closure is anti-symmetric.

A reflexive relation on a nonempty set can neither be irreflexive, nor asymmetric ( is called asymmetric if implies not ), nor antitransitive ( is antitransitive if implies not ).

Examples

Examples of reflexive relations include:
* "is equal to" (equality)

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