On S = {3, 5, 7, 8, 9, 10, 12, 27, 30, 70} 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-maksimal elements.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

On S = {3, 5, 7, 8, 9, 10, 12, 27, 30, 70} 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-maksimal elements.
(iv) Find all non-empty subsets U ⊆ S, so that 3 is an R-lowerbound of U.
(v) Is R a lattice?

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