Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. 2. let d be a relation on the natural numbers n de

2. Let D be a relation on the natural numbers N de?ned by D = {(m,n)...

80.2K

Verified Solution

Question

Advance Math

2. Let D be a relation on the natural numbers N de?ned by D ={(m,n) : m | n} (i.e., D(m,n) is true when n is divisible by m. Forthis problem, you’ll be proving that D is a partial order. Thismeans that you’ll need to prove that it is re?exive,anti-symmetric, and transitive.

(a) Prove that D is re?exive. (Yes, you already did this problemon one of the minihomework assignments. You don’t have to redo theproblem, but you should at least copy over your answer from thatassignments to this one.)

(b) Prove that D is anti-symmetric. You may use the followingfact: for any two natural numbers m and n, if m·n = 1, then m = 1and n = 1. (Note that D is only anti-symmetric because the domainis the natural numbers. If we switched to the domain of integers,then things would be completely di?erent.)

(c) Prove that D is transitive. (You’ve probably done a problemalready that is almost exactly the same as this.)

Answer & Explanation Solved by verified expert
4.5 Ratings (881 Votes)
    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

Q

Q5 7 In a population where the proportion of individuals who are susceptible to malaria...

Biology
Q

35 The cardiovascular system plays a role in temperature regulation of the body True or...

Biology
Q

Illustration 4 A series circuit consists of a resistance of 1502 an inductance of 0...

Physics
Q

49 Figure shows the position of a particle moving on the x axis as a...

Physics
Q

a 2x 3x y 5 Jadratics using the quadratic formula b 5x 80 y

Basic Math
Q

High blood pressure: A national survey reported that 31% of adults in a certain country...

Statistics
Q

Multiply and simplify Assume that no radicands were formed by raising negative numbers to even...

Algebra
Q

TB MC Qu. 16-148 (Algo) Dazzle, Incorporated produces beads for... Dazzle. Incorporated produces beads for...

Accounting
Q

Bradburn Corporation was formed 5 years ago through a public subscription of common stock. Daniel...

Accounting
Q

Which of the following procedures would be least likely to be included in an auditor's...

Accounting
Q

1. A una tasa de inters del 10% anual, a cunto equivalen $ 10,000 de...

Finance
Q

11. Your 2018 federal gross income (W2 wages, capital gains, and dividends) would be closest...

Finance