an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
The relation "is equal to" is the canonical example of an equivalence relation,
where for any objects a, b, and c:
a = a (reflexive property),
if a = b then b = a (symmetric property), and
if a = b and b = c, then a = c (transitive property).
As a consequence of the reflexive, symmetric, and transitive properties,
any equivalence relation provides a partition of the underlying set into
disjoint equivalence classes.
Two elements of the given set are equivalent to each other, if and only if
they belong to the same equivalence class.
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