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*Definition:*
The relation induced by a partition `D` is the set of all pairs of
elements of the same block of `D`:

x~_{D}y: <=>existsdinD:xind/\yind.

*Proposition:*
Let `D` be a partition of `S`.
The relation induced by `D` is an equivalence relation
on `S`:

forallS,D:Dis partition ofS=>~ _{D}is equivalence relation onS.

*Every partition defines an equivalence relation.*

Author: Wolfgang Schreiner

Last Modification: January 12, 2000