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Let K = {a, b, c, d, e}. Find, for each part of the question, an example of an object that satisfies the following conditions, or prove that none exists: (b) a non-planar tree with vertex set K; a 4-colourable graph with vertex set K that is not 3-colourable;

Let K = {a, b, c, d, e}. Find, for each part of the question, an example of an object that satisfies the following conditions, or prove that none exists: (b) a non-planar tree with vertex set K; a 4-colourable graph with vertex set K that is not 3-colourable;

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 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...
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1. Let K = {a, b, c, d, e}. Find, for each part of the question, an example of an object that satisfies the following conditions, or prove that none exists: (a) (b) (c) (d) a partial order on K such that, for all pairs x, y E K satisfying both x≤y and xy, the condition y <a holds as well; an equivalence relation ~on K such that |K/~= 3. (e) infinite; a non-planar tree with vertex set K; a 4-colourable graph with vertex set K that is not 3-colourable; a surjective function h: RK such that the set h-¹(a) is countably
Transcribed Image Text:1. Let K = {a, b, c, d, e}. Find, for each part of the question, an example of an object that satisfies the following conditions, or prove that none exists: (a) (b) (c) (d) a partial order on K such that, for all pairs x, y E K satisfying both x≤y and xy, the condition y <a holds as well; an equivalence relation ~on K such that |K/~= 3. (e) infinite; a non-planar tree with vertex set K; a 4-colourable graph with vertex set K that is not 3-colourable; a surjective function h: RK such that the set h-¹(a) is countably
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