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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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