Determine whether the following relations are equivalence relations. For those relations that are equivalence relations, describe the equivalence classes. (b) {(x, y) ∈ R × R : |x| = |y|}, where |x| is the absolute value of x
Determine whether the following relations are equivalence relations. For those relations that are equivalence relations, describe the equivalence classes. (b) {(x, y) ∈ R × R : |x| = |y|}, where |x| is the absolute value of x
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 15E: Let A=R0, the set of all nonzero real numbers, and consider the following relations on AA. Decide in...
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Question
Determine whether the following relations are equivalence relations. For those relations
that are equivalence relations, describe the equivalence classes.
(b) {(x, y) ∈ R × R : |x| = |y|}, where |x| is the absolute value of x
Expert Solution
Step 1
Consider the given relation is given as:
Step 2
Show that the given relation is an equivalence classes.
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