Solution Found!

Math / Modern Algebra: An Introduction 6 / Chapter 9 / Problem 9.5

Modern Algebra: An Introduction | 6th Edition | ISBN: 9780470384435 | Authors: John R. Durbin

Change Question

For points with coordinates (XI. YI) and (X2, Y2) in a plane with rectan'gular

Chapter 9, Problem 9.5

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

For points with coordinates (XI. YI) and (X2, Y2) in a plane with rectan'gular coordinate system,let (XI, YI) ~ (X2, Y2) mean that YI = Y2(a) Prove that ~ is an equivalence relation on the set of points in the plane. State clearly theproperties of the relation = on JR that are used in the proof.(b) Describe the equivalence classes geometrically.(c) Give a complete set of equivalence class representatives.

Questions & Answers

QUESTION:

For points with coordinates (XI. YI) and (X2, Y2) in a plane with rectan'gular coordinate system,let (XI, YI) ~ (X2, Y2) mean that YI = Y2(a) Prove that ~ is an equivalence relation on the set of points in the plane. State clearly theproperties of the relation = on JR that are used in the proof.(b) Describe the equivalence classes geometrically.(c) Give a complete set of equivalence class representatives.

ANSWER:

Step 1 of 3

(a)

As per the reflexive property of on , it is known that for all which gives for all and therefore, is reflexive.

If then . As per the symmetric property of on , gives which also gives and therefore, is symmetric.

If and then and .as per the transitivity of on , gives , , and and then . Therefore, is transitive.

Hence, is an equivalence relation on .

Study Tools You Might Need

Chapter: 20 Problem: 53

College Physics 1
Problem 53PE Some makes of older cars have 6.00-V electrical systems. (a) What is the hot resistance of a 30.0-W headlight in such a car? (b) What current flows through it?

Chapter: 4 Problem: 4.1.14

BSCS Biology: A Molecular Approach 9
Why are chemoautotrophs rare among familiar organisms?

Chapter: 26 Problem: 1

Glencoe Accounting: First Year Course, Student Edition 1
Promissory Notes a. Name the two parties to a promissory note. Which party issues the note? Which party receives the note? b. Describe a situation in which a business might (a) receive a promissory note and (b) issue a promissory note.

Chapter: 2 Problem: 8

Principles of Economics 1
Explain why scarcity leads to tradeoffs.

Chapter: 14 Problem: 1

Principles of Accounting, Volume 1: Financial Accounting
Which of the following is not a characteristic that sets preferred stock apart from common stock? A. voting rights B. dividend payments C. transferability D. ownership

Chapter: 34 Problem: 22

Biology 2e by Openstax
What is the role of the accessory organs in digestion?

Chapter: 9 Problem: 87

Plant Systematics 3
What is the difference between a silique and a silicle? What family do they occur in?

Chapter: 20 Problem: 1

Biochemistry 9
Briefly summarize the steps in the electron transport chain from NADH to oxygen.

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account