Determine the equivalence classes of each equivalence relation below: (a) {(a, b) ∈ Z × Z : a ≡ b mod 2 ∧ a ≡ b mod 4} (b) {(x, y) ∈ R × R : x = y ∨ x = −y} (c) {(x, y) ∈ R × R : (x < 0 ∧ y < 0) ∨ (x ≥ 0 ∧ y ≥ 0)} (Z = the set of integers, R = the set of real numbers
Determine the equivalence classes of each equivalence relation below: (a) {(a, b) ∈ Z × Z : a ≡ b mod 2 ∧ a ≡ b mod 4} (b) {(x, y) ∈ R × R : x = y ∨ x = −y} (c) {(x, y) ∈ R × R : (x < 0 ∧ y < 0) ∨ (x ≥ 0 ∧ y ≥ 0)} (Z = the set of integers, R = the set of real numbers
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 23E: 23. Let be the equivalence relation on defined by if and only if there exists an element in ...
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Determine the equivalence classes of each equivalence relation below: (a) {(a, b) ∈ Z × Z : a ≡ b mod 2 ∧ a ≡ b mod 4} (b) {(x, y) ∈ R × R : x = y ∨ x = −y} (c) {(x, y) ∈ R × R : (x < 0 ∧ y < 0) ∨ (x ≥ 0 ∧ y ≥ 0)} (Z = the set of integers, R = the set of real numbers
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