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solve question (g),(h) with complete explanation asap

solve question (g),(h) with complete explanation asap

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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solve question (g),(h) with complete explanation asap
Let (A= (2, 4, 6, 9, 12, 18, 27, 36, 48, 60, 72), R) be a partially ordered set, where the relation R is defined by: XRy if and only if y divides x. a) Find all the minimal elements. b) Find all the maximal elements. c) Is there a greater element? If yes, specify d) Is there a smaller element? If yes specify e) Find all upper bounds of {60, 72). f) Find all lower bounds of (2, 9). g) Find the supremum of (60, 72) if it exists. h) Find the infimum of (2, 9) if it exists.
Transcribed Image Text:Let (A= (2, 4, 6, 9, 12, 18, 27, 36, 48, 60, 72), R) be a partially ordered set, where the relation R is defined by: XRy if and only if y divides x. a) Find all the minimal elements. b) Find all the maximal elements. c) Is there a greater element? If yes, specify d) Is there a smaller element? If yes specify e) Find all upper bounds of {60, 72). f) Find all lower bounds of (2, 9). g) Find the supremum of (60, 72) if it exists. h) Find the infimum of (2, 9) if it exists.
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