In the Cartesian plane = {(x, y): x, y ER} consisting of points with rectangularcoordinates (x, y), define the relation by (x1, y₁) ~ (x2, Y2)x1 = x2.(c) Prove that is an equivalence relation on the set P.(d) Describe the equivalence classes geometrically.

Answered: Image /qna-images/answer/6082977e-e8a5-464d-8d0e-aef9b2bb84d8.jpg

Answered: In the Cartesian plane = {(x, y): x,y E…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 12E: Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and...

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In the Cartesian plane = {(x, y): x,y E R} consisting of points with rectangular coordinates (x, y), define the relation by (1, ₁)~ (x2, Y2) I1=I₂. (c) Prove that is an equivalence relation on the set P. (d) Describe the equivalence classes geometrically.