17. (15pts) Let relation G be a subset of the cross product of the natural numbers with the natural numbers: GCNxN. E 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 (d) Antisymmetric YES NO (e) Irreflexive YES NO (f) Asymmetric YES NO
17. (15pts) Let relation G be a subset of the cross product of the natural numbers with the natural numbers: GCNxN. E 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 (d) Antisymmetric YES NO (e) Irreflexive YES NO (f) Asymmetric YES NO
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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Question
17-
![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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb017a202-bb10-4722-a8c7-7967a12b195b%2Ff129c9ad-2ad6-46a6-b8d7-0ba3d95a8bf8%2Fixpgxgp_processed.jpeg&w=3840&q=75)
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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