Determine whether the following relations are equivalence relations. For those relations that are equivalence relations, describe the equivalence classes. (a) {(x, y) ∈ Z × Z : x + y is an even integer} (b) {(x, y) ∈ R × R : |x| = |y|}, where |x| is the absolute value of x. (c) {(x, y) ∈ C × C : |x| = |y|}, where |x| is the length of x.

Determine whether the following relations are equivalence relations. For those relations that are equivalence relations, describe the equivalence classes. (a) {(x, y) ∈ Z × Z : x + y is an even integer} (b) {(x, y) ∈ R × R : |x| = |y|}, where |x| is the absolute value of x. (c) {(x, y) ∈ C × C : |x| = |y|}, where |x| is the length of x.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 21E: 21. A relation on a nonempty set is called irreflexive if for all. Which of the relations in...

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