7. Answer these questions for the poset ({2, 6, 8, 12, 18, 36, 48, 60, 96), ), where "|" represents the "divides" relation. (Hint: create a Hasse diagram.) a. Find the maximal elements. b. Find the minimal elements. c. Is there a greatest element? d. Is there a least element? e. Find all upper bounds of {6, 8).

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 17E: In each of the following parts, a relation R is defined on the power set (A) of the nonempty set A....
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7.
Answer these questions for the poset ({2, 6,8,12, 18, 36, 48, 60, 96},|), where "|"
represents the "divides" relation. (Hint: create a Hasse diagram.)
a. Find the maximal elements.
b. Find the minimal elements.
c. Is there a greatest element?
d. Is there a least element?
e. Find all upper bounds of {6, 8}.
f.
Find the least upper bound of {6, 8}, if it exists.
g. Find all lower bounds of {48, 72}.
h. Find the greatest lower bound of {48, 72}, if it exists.
Transcribed Image Text:7. Answer these questions for the poset ({2, 6,8,12, 18, 36, 48, 60, 96},|), where "|" represents the "divides" relation. (Hint: create a Hasse diagram.) a. Find the maximal elements. b. Find the minimal elements. c. Is there a greatest element? d. Is there a least element? e. Find all upper bounds of {6, 8}. f. Find the least upper bound of {6, 8}, if it exists. g. Find all lower bounds of {48, 72}. h. Find the greatest lower bound of {48, 72}, if it exists.
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