Answer 11b 11. Let A be a nonempty set and let ~ be an equivalence relation on A. Proveeach of the following:(a) For each a, b e A, a × b if and only if [a] N [b] = Ø.(b) For each a, b e A, if [a] # [b], then [a] N [b] = Ø.(c) For each a, b e A, if [a] N [b] # Ø then [a] = [b].

Name: Answer 11b 11. Let A be a nonempty set and let ~ be an equivalence rel
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Description: Answer 11b 11. Let A be a nonempty set and let ~ be an equivalence relation on A. Proveeach of the following:(a) For each a, b e A, a × b if and only if [a] N [b] = Ø.(b) For each a, b e A, if [a] # [b], then [a] N [b] = Ø.(c) For each a, b e A, if [

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11. Let A be a nonempty set and let ~ be an equivalence relation on A. Prove each of the following: (a) For each a, b eE A, a × b if and only if [a] N [b] = Ø. (b) For each a, b e A, if [a] # [b], then [a] N [b] = Ø. (c) For each a, b e A, if [a] N [b] 7 Ø then [a] = [b].

11. Let A be a nonempty set and let ~ be an equivalence relation on A. Prove each of the following: (a) For each a, b eE A, a × b if and only if [a] N [b] = Ø. (b) For each a, b e A, if [a] # [b], then [a] N [b] = Ø. (c) For each a, b e A, if [a] N [b] 7 Ø then [a] = [b].

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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