Problem 1. Let n be a fixed positive integer and let EC₁ = {[0]n, [1]n, ..., [n − 1]n}. If x € [a], and y € [b]n, prove that [ab] = [xy]n. (Use the fact that ab - xy = (ab - xy) + (bx − bx) .) - Proof: Since the equivalence classes modulo n form a partition of Z, we only need to show that [xy]n € [ab]n. Define n according to the following formula: For integers a, b let [a], \n [b]n conclude that this rule defines a binary operation on the set ECn. = [ab]n. Problem 1 allows us to

Problem 1. Let n be a fixed positive integer and let EC₁ = {[0]n, [1]n, ..., [n − 1]n}. If x € [a], and y € [b]n, prove that [ab] = [xy]n. (Use the fact that ab - xy = (ab - xy) + (bx − bx) .) - Proof: Since the equivalence classes modulo n form a partition of Z, we only need to show that [xy]n € [ab]n. Define n according to the following formula: For integers a, b let [a], \n [b]n conclude that this rule defines a binary operation on the set ECn. = [ab]n. Problem 1 allows us to

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 38E

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