Define a relation on R^2 by (x1, y1) ~ (x2, y2) if y1 = y2. This is an equivalence relation. (You do not need to prove this claim.) a. Explain why all points on the x-axis belong to the same equivalence class. b. Prove that if p1, p2 are two distinct points on the line y = 2x + 5, then [p1] ≠ [p2]. c. Define a function f : R -> R^2 /~ such that f is a bijection. (You don’t have to prove your function is a bijection

Define a relation on R^2 by (x1, y1) ~ (x2, y2) if y1 = y2. This is an equivalence relation. (You do not need to prove this claim.) a. Explain why all points on the x-axis belong to the same equivalence class. b. Prove that if p1, p2 are two distinct points on the line y = 2x + 5, then [p1] ≠ [p2]. c. Define a function f : R -> R^2 /~ such that f is a bijection. (You don’t have to prove your function is a bijection

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

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