Let X = {-2, 0, 2} and let P(X) be the power set of x (the set of all subsets of X). A relation R is defined on P(X) as follows: For all S, T ∈ P(X), SRT ⇔ the sum of elements in S = the sum of the elements in T. (a) Prove that R is transitive. (b) Write down the equivalence classes of R.

Let X = {-2, 0, 2} and let P(X) be the power set of x (the set of all subsets of X). A relation R is defined on P(X) as follows: For all S, T ∈ P(X), SRT ⇔ the sum of elements in S = the sum of the elements in T. (a) Prove that R is transitive. (b) Write down the equivalence classes of R.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.3: Subgroups

Problem 23E: 23. Let be the equivalence relation on defined by if and only if there exists an element in ...

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(a) Prove that R is transitive.

(b) Write down the equivalence classes of R.

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