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6. On S = {2, 4, 6, 10, 12, 20, 30, 60} we work with the divisibility relation R: xRyx divides y. (i) Draw the Hasse diagram of R. (ii) Find all R-minimal elements. (iii) Find all R-maximal elements.

6. On S = {2, 4, 6, 10, 12, 20, 30, 60} we work with the divisibility relation R: xRyx divides y. (i) Draw the Hasse diagram of R. (ii) Find all R-minimal elements. (iii) Find all R-maximal elements.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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On S = f2; 4; 6; 10; 12; 20; 30; 60g we work with the divisibility relation R:
xRy , x divides y:
(i) Draw the Hasse diagram of R.
(ii) Find all R-minimal elements.
(iii) Find all R-maximal elements.
(iv) Find all non-empty subsets U  S, so that 6 is an R-lowerbound of U.
(v) Let A = f6; 10; 12g. If A admits an R-supremum,  nd it. If A admits an R-in mum,  nd it.
(vi) Is R a lattice?

6. On S = {2, 4, 6, 10, 12, 20, 30, 60} we work with the divisibility relation R: xRy ⇒ x divides y. (i) Draw the Hasse diagram of R. (ii) Find all R-minimal elements. (iii) Find all R-maximal elements. (iv) Find all non-empty subsets UC S, so that 6 is an R-lowerbound of U. (v) Let A = {6, 10, 12}. If A admits an R-supremum, find it. If A admits an R-infimum, find it. (vi) Is R a lattice?
Transcribed Image Text:6. On S = {2, 4, 6, 10, 12, 20, 30, 60} we work with the divisibility relation R: xRy ⇒ x divides y. (i) Draw the Hasse diagram of R. (ii) Find all R-minimal elements. (iii) Find all R-maximal elements. (iv) Find all non-empty subsets UC S, so that 6 is an R-lowerbound of U. (v) Let A = {6, 10, 12}. If A admits an R-supremum, find it. If A admits an R-infimum, find it. (vi) Is R a lattice?
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