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8. For a given set A, and an equivalence relation R defined on A, select one property and prove it. a) Every element of A belongs to some equivalence class. b) Two elements are equivalent if and only if their equivalence classes are equal c) Two equivalence classes are either identical or they are disjoint.

8. For a given set A, and an equivalence relation R defined on A, select one property and prove it. a) Every element of A belongs to some equivalence class. b) Two elements are equivalent if and only if their equivalence classes are equal c) Two equivalence classes are either identical or they are disjoint.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 10E: In Exercises , a relation is defined on the set of all integers. In each case, prove that is an...
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8. For a given set A, and an equivalence relation R defined on A, select one property and prove it. a) Every element of A belongs to some equivalence class. b) Two elements are equivalent if and only if their equivalence classes are equal c) Two equivalence classes are either identical or they are disjoint.
Transcribed Image Text:8. For a given set A, and an equivalence relation R defined on A, select one property and prove it. a) Every element of A belongs to some equivalence class. b) Two elements are equivalent if and only if their equivalence classes are equal c) Two equivalence classes are either identical or they are disjoint.
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