Determine, with justification, whether the following relations are equivalence relations. If so, describe the partition arising from the equivalence relation. (a) x ∼ y in R if x ≥ y (b) n ∼ m in Z if |n| = |m|.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 3TFE: True or False Label each of the following statements as either true or false. If is an equivalence...
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Determine, with justification, whether the following relations are equivalence relations. If so, describe the partition arising from the equivalence relation.

(a) x ∼ y in R if x ≥ y

(b) n ∼ m in Z if |n| = |m|.

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