Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. in this problem we consider another way to think a

In this problem we consider another way to think about the rational numbers. Normally we would...

50.1K

Verified Solution

Question

Advance Math

In this problem we consider another way to think about therational numbers. Normally we would write fractions as p/q for p ?Z and q ? N. In this problem we represent fractions as orderedpairs. So let S = {(p, q)|p ? Z and q ? N}.

For ordered pairs (p, q) and (r, s) in S define (p, q)R(r, s) ifand only if ps = qr.

You should think about how this is related to the test that twofractions are equal.

a. Prove that R is an equivalence relation on S.

b. What is the equivalence class that contains (0, 1)?

c. What is the equivalence class that contains (2, 1)? Nowdefine a partial order (p, q) ? (r, s) for (p, q) ? S and (r, s) ?S. Answer each of the following question and prove your result.

d. Is this a reflexive relation?

e. Is it symmetric?

f. Is it antisymmetric?

g. Is this a transitive relation?

Answer & Explanation Solved by verified expert
4.3 Ratings (760 Votes)
Forthe 2nd part of the question The    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Physics
1.2K views

Phy Section B This section contains 15 SINGLE CORRECT TYPF questions Out of these 15...

Basic Math
1.2K views

Find the cost of the monthly rent for a two bedroom apartment in 30 years...

Basic Math
1.2K views

Two points P and Q in the Argand diagram rep- resent complex numbers z and...

Statistics
1.2K views

In the United States there has historically been a strong relationship between smoking and education...

Calculus
1.2K views

Find the points on the ellipse 4x 2y 1 where f x y xy has...

Accounting
1.2K views

The Management of Carla Vista Manufacturing Company is evaluating two forklift systems to use in...

Accounting
1.2K views

11ABC Corporation has two divisions: Division X and Division Z. Data from the most recent...

Accounting
1.2K views

received $570,000 cash from owner, m. Balfort, in exchange for capital. Opened a new checking...

Accounting
1.2K views

Help please Web Wizard, Incorporated, has provided information...

Accounting
1.2K views

The Dakota Corporation had a 2021 taxable income of $28,500,000 from operations after all operating...

Finance
1.2K views

i need the answer consider that a call option on non-dividend paying...

Finance
1.2K views

Problem 3.3 A stock price is currently $50. It is known that at the end...