Answered: (b) Let {A₁, A2,...} be a partition of…

(b) Let {A₁, A2,...} be a partition of a set X, and R the relation {(x, y) = X²: there exists j such that x € A, and y ≤ A; }. Prove that R is an equivalence relation.

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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Question

(b) Let {A₁, A2,...} be a partition of a set X, and R the relation
{(x, y) = X²: there exists j such that x € A, and y € A; }.
Prove that R is an equivalence relation.

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