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Let A = {1, 2, 3, 4, 5, 6}. Which statement below is true? (Hint: The equivalence classes of an equivalence relation on A gives a partition of A, or in other words, their union is A and they are pairwise disjoint.) There is an equivalence relation on A whose equivalence classes are: {1,2},{3,5}, {6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {3, 5}, {4,6}. There is an equivalence relation on A whose equivalence classes are: {1,2,3}, {5}, {5,6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {5}, {4,6}.

Let A = {1, 2, 3, 4, 5, 6}. Which statement below is true? (Hint: The equivalence classes of an equivalence relation on A gives a partition of A, or in other words, their union is A and they are pairwise disjoint.) There is an equivalence relation on A whose equivalence classes are: {1,2},{3,5}, {6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {3, 5}, {4,6}. There is an equivalence relation on A whose equivalence classes are: {1,2,3}, {5}, {5,6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {5}, {4,6}.

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 3E: a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the...
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Let A = {1, 2, 3, 4, 5, 6}. Which statement below is true? (Hint: The equivalence classes of an equivalence relation on A gives a partition of A, or in other words, their union is A and they are pairwise disjoint.) There is an equivalence relation on A whose equivalence classes are: O {1,2},{3,5},{6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {3, 5}, {4, 6}. There is an equivalence relation on A whose equivalence classes are: O {1,2,3}, {5},{5,6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {5}, {4,6}.
Transcribed Image Text:Let A = {1, 2, 3, 4, 5, 6}. Which statement below is true? (Hint: The equivalence classes of an equivalence relation on A gives a partition of A, or in other words, their union is A and they are pairwise disjoint.) There is an equivalence relation on A whose equivalence classes are: O {1,2},{3,5},{6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {3, 5}, {4, 6}. There is an equivalence relation on A whose equivalence classes are: O {1,2,3}, {5},{5,6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {5}, {4,6}.
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