Answer to Question #146317 in Discrete Mathematics for Promise Omiponle

Question #146317
Suppose S is a set, and P={S} is a partition of S. Find the equivalence relation R corresponding to P.
1
Expert's answer
2020-11-29T18:20:20-0500

S be a set.

P={S}\{S\} is a partition on S.

The equivalence relation R corresponding to P on S is following

For each aS\in S we denote the equivalence class of a as [a], which can be defined as,

[a]={xSxRa}\{x\in S| xRa\} =S. This is the only equivalence class.

(Here R is defined on S, xRaxRa x,aS)\Leftrightarrow x,a\in S)



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