Equivalence Class Definition/Meaning:
A subset of a set S (on which an equivalence relation is
defined) that consists of all the elements of S that are equivalent to each
other, and to no other elements of S. An equivalence relation provides a
partitioning (see covering) of a set into a number of mutually
disjoint
equivalence classes.
The relationship "has the same surname as" defined on the
set of people produces an equivalence class consisting of all those
with Jones as surname, another consisting of those with Smith as surname, and so
on.
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