For simultaneously reflexive, symmetric and transitive relations. Use it with the tag (relations).

An equivalence relation is a binary relation $R$ on a set $A$ that is reflexive, symmetric and transitive:

  • $(\forall a\in A):aRa$ (reflexive)
  • $(\forall a,b\in A):aRb \implies bRa$ (symmetric)
  • $(\forall a,b,c\in A):aRb\wedge bRc \implies aRc$ (transitive)
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