Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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16. (10pts) Prove using the First Principle of Math Induction (weak induction): 6.7 -2.3" is divisible by 4 for all integers n ≥ 1 17. (15pts) Let relation G be a subset of the cross product of the natural numbers with the natural numbers: GCNX N. Define relation R as: (a, b) e G⇒ [a+b≥ 18] You may assume the natural numbers include 0. Determine if the relation is each of these: (a) Reflexive YES NO (b) Symmetric YES NO (c) Transitive YES NO YES NO (d) Antisymmetric (e) Irreflexive YES NO (f) Asymmetric YES NO 101) S 18. (15pts) (a) How many simple non-isomorphic simple undirected graphs with five vertices and three edges are there? Draw them all (hint: less than 10) (b) How many simple non-isomorphic directed graphs with five vertices and three edges are there? Draw them all. (hint: less than 20)
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Transcribed Image Text:16. (10pts) Prove using the First Principle of Math Induction (weak induction): 6.7 -2.3" is divisible by 4 for all integers n ≥ 1 17. (15pts) Let relation G be a subset of the cross product of the natural numbers with the natural numbers: GCNX N. Define relation R as: (a, b) e G⇒ [a+b≥ 18] You may assume the natural numbers include 0. Determine if the relation is each of these: (a) Reflexive YES NO (b) Symmetric YES NO (c) Transitive YES NO YES NO (d) Antisymmetric (e) Irreflexive YES NO (f) Asymmetric YES NO 101) S 18. (15pts) (a) How many simple non-isomorphic simple undirected graphs with five vertices and three edges are there? Draw them all (hint: less than 10) (b) How many simple non-isomorphic directed graphs with five vertices and three edges are there? Draw them all. (hint: less than 20)
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