Define S to be the following relation on R[x]: S = {(f, g) = R[x]²: (x-3) divides (g-f) in R[x]}. You may assume that S is an equivalence relation. i. Prove that, if (f₁, f₂) € S and (9₁, 92) € S for some f₁, f2, 91, 92 € R[x], then also (f₁ + 91, f2 +9₂) € S. vivalenos simile
Define S to be the following relation on R[x]: S = {(f, g) = R[x]²: (x-3) divides (g-f) in R[x]}. You may assume that S is an equivalence relation. i. Prove that, if (f₁, f₂) € S and (9₁, 92) € S for some f₁, f2, 91, 92 € R[x], then also (f₁ + 91, f2 +9₂) € S. vivalenos simile
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 28E
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