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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) a non-planar tree with vertex set K;

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) a non-planar tree with vertex set K;

Advanced Engineering Mathematics
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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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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