e) Is it possible for a graph to be a tree and complete bipartite graph at the same time? f) Is the relation R, defined on the set of real numbers by xRy if 2x + y = 3. antisymmetric? g) Is it possible for a poset to have multiple maximal elements?

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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Decide if the statement is True or False. Justify your answer. Explain why is it true or
why not, and give an example/counterexample where necessary.

e) Is it possible for a graph to be a tree and complete bipartite graph at the same time?
f) Is the relation R, defined on the set of real numbers by xRy if 2x + y = 3.
antisymmetric?
g) Is it possible for a poset to have multiple maximal elements?
Transcribed Image Text:e) Is it possible for a graph to be a tree and complete bipartite graph at the same time? f) Is the relation R, defined on the set of real numbers by xRy if 2x + y = 3. antisymmetric? g) Is it possible for a poset to have multiple maximal elements?
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