Let S be a nonempty set and let P = {S1, S2, . . . , Sk} be a partition of S, where k 1

Chapter 5, Problem 15

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Let S be a nonempty set and let P = {S1, S2, . . . , Sk} be a partition of S, where k 1. Define a relation R on S by a R b if a, b Si for some i with 1 i k. (a) Prove that R is an equivalence relation. (b) Describe the distinct equivalence classes resulting from R.

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