(a) R₁ = {(x,y): x, y Є Z, 2 | (x² + y²)}. (b) R₂ = {(x, y): x,yЄZ,4 | (x+3y)}. (c) R3 = {(x, y): x, y Є Z, r² = y²(mod 4)}. B msi M

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 56E
Question
Prove relation B is an equivalence relation
(a) R₁ = {(x,y): x, y Є Z, 2 | (x² + y²)}.
(b) R₂ = {(x, y): x,yЄZ,4 | (x+3y)}.
(c) R3 = {(x, y): x, y Є Z, r² = y²(mod 4)}.
B
msi
M
Transcribed Image Text:(a) R₁ = {(x,y): x, y Є Z, 2 | (x² + y²)}. (b) R₂ = {(x, y): x,yЄZ,4 | (x+3y)}. (c) R3 = {(x, y): x, y Є Z, r² = y²(mod 4)}. B msi M
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