LARA

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Equivalence relation

An equivalence relation $\sim$ is a binary relation on set $A$ (that is, a subset of $A^2$) that is reflexive, symmetric, and transitive, that is, the following three properties hold:

  • $x \sim x$
  • $x \sim y\ \rightarrow\ y \sim x$
  • $x \sim y\ \land\ y \sim z\ \rightarrow\ x \sim z$