Discrete Mathematics with Graph Theory ...3rd EditionEdgar Goodaire, Michael Parmenter Publisher: PEARSONISBN: 9780134689555
Discrete Mathematics with Graph Theory ...
Solutions for Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Problem 1TFQ:
If you want to prove a statement is true, it is enough to find 867 examples where it is true.Problem 2TFQ:
True/False Questions
2. If you want to prove a statement is false, it is enough to find one example...Problem 6TFQ:
The contrapositive of A Bis B A.Problem 7TFQ:
A Bis true if and only if its contrapositive is true.Problem 8TFQ:
True/False Questions
8. is a rational number.
Problem 9TFQ:
True/False Questions
9. 3.141 is a rational number.
Problem 10TFQ:
True/False Questions
10. If and are irrational numbers, then must be an irrational number.
Problem 11TFQ:
True/False Questions
11. The statement “Every real number is rational” can be proved false with a...Problem 12TFQ:
The statement There exists an irrational number that is not the square root of an integer can be...Problem 1E:
What is the hypothesis and what is the conclusion in each of the following implications?
The sum of...Problem 2E:
2. In each part of Exercise 1, what condition is necessary for what? What condition is sufficient...Problem 3E:
Exhibit a counterexample to each of the following statements. x2=4x=2. a and b integers and...Problem 4E:
Consider the following two statements: A: The square of every real number is positive. B: There...Problem 5E:
Determine whether the following implication is true. x is an even integer x+2 is an even integer.Problem 7E:
7. Answer Exercise 5 with replaced by .
Problem 8E:
Consider the statement A: If n is an integer, nn+1 is not an integer. Is A true or false? Either...Problem 9E:
9. Let be an integer greater than 1 and consider the statement “A: prime is necessary for to be...Problem 10E:
10. A theorem in calculus states that every differentiable function is continuous. State the...Problem 11E:
11. Let be an integer, . A certain mathematical theorem asserts that statements are equivalent.
(a)...Problem 12E:
Consider the assertions A: For every real number x, there exists an integer n such that nxn+1. B:...Problem 13E:
Answer Exercise 12 with A and B as follows. A: There exists a real number y such that yx for every...Problem 14E:
14. Answer true or false and supply a direct proof or a counterexample to each of the following...Problem 15E:
Prove that n an even integer n2+3n is an even integer. What is the converse of the implication in...Problem 16E:
16. (a) Let be an integer. Show that either or is even.
(b) Show that is even for any integer.
Problem 18E:
Prove that 2x24x+30 for any real number x.Problem 19E:
19. Let and be integers. By examining the four cases
i. both even,
ii. both odd,
iii. even, odd,...Problem 22E:
Prove that if n is an odd integer then there is an integer m such that n=4m+1 or n=4m+3. [Hint:...Problem 23E:
23. Prove that if is an odd integer, there is an integer such that or or or. (You may use the...Problem 24E:
24. Prove that there exists no smallest positive real number. [Hint: Find a proof by...Problem 26E:
26. (For students who have studied linear algebra) Suppose 0 is an eigenvalue of a matrix A. Prove...Problem 27E:
27. (a) Suppose and are integers such that . Prove that and .
(b) Prove that is not the square of a...Problem 28E:
Suppose a and b are integers such that a+b+ab=0. Prove that a=b=0 or a=b=2. Give a direct proof.Problem 30E:
30. Suppose that is a rational number and that is an irrational number. Prove that is irrational.
Browse All Chapters of This Textbook
Chapter 0 - Yes, There Are Proofs!Chapter 0.1 - Compund StatementsChapter 0.2 - Proofs In MathematicsChapter 1 - LogicChapter 1.1 - Truth TablesChapter 1.2 - The Algebra Of PropositionsChapter 1.3 - Logical ArgumentsChapter 2 - Sets And RelationsChapter 2.1 - SetsChapter 2.2 - Operations On Sets
Chapter 2.3 - Binary RelationsChapter 2.4 - Equivalence RelationsChapter 2.5 - Partial OrdersChapter 3 - FunctionsChapter 3.1 - Basic TerminologyChapter 3.2 - Inverses And CompositionChapter 3.3 - One-to-one Correspondence And The Cardinality Of A SetChapter 4 - The IntegersChapter 4.1 - The Division AlgorithmChapter 4.2 - Divisibility And The Euclidean AlgorithmChapter 4.3 - Prime NumbersChapter 4.4 - CongruenceChapter 4.5 - Applications Of CongruenceChapter 5 - Induction And RecursionChapter 5.1 - Mathematical InductionChapter 5.2 - Recursively Defined SequencesChapter 5.3 - Solving Recurrence Relations; The Characteristic PolynomialChapter 5.4 - Solving Recurrence Relations; Generating FunctionsChapter 6 - Principles Of CountingChapter 6.1 - The Principle Of Inclusion-exclusionChapter 6.2 - The Addition And Multiplication RulesChapter 6.3 - The Pigeonhole PrincipleChapter 7 - Permutations And CombinationsChapter 7.1 - PermutationsChapter 7.2 - CombinationsChapter 7.3 - Elementary ProbabilityChapter 7.4 - Probability TheoryChapter 7.5 - RepetitionsChapter 7.6 - DerangementsChapter 7.7 - The Binomial TheoremChapter 8 - AlgorithmsChapter 8.1 - What Is An Algorithm?Chapter 8.2 - ComplexityChapter 8.3 - Searching And SortingChapter 8.4 - Enumeration Of Permutations And CombinationsChapter 9 - GraphsChapter 9.1 - A Gentle IntroductionChapter 9.2 - Definitions And Basic PropertiesChapter 9.3 - IsomorphismChapter 10 - Paths And CircuitsChapter 10.1 - Eulerian CircuitsChapter 10.2 - Hamiltonian CyclesChapter 10.3 - The Adjacency MatrixChapter 10.4 - Shortest Path AlgorithmsChapter 11 - Applications Of Paths And CircuitsChapter 11.1 - The Chinese Postman ProblemChapter 11.2 - DigraphsChapter 11.3 - Rna ChainsChapter 11.4 - TournamentsChapter 11.5 - Scheduling ProblemsChapter 12 - TreesChapter 12.1 - Trees And Their PropertiesChapter 12.2 - Spanning TreesChapter 12.3 - Minimum Spanning Tree AlgorithmsChapter 12.4 - Acyclic Digraphs And Bellman's AlgorithmChapter 12.5 - Depth-first SearchChapter 12.6 - The One-way Street ProblemChapter 13 - Planar Graphs And ColoringsChapter 13.1 - Planar GraphsChapter 13.2 - Coloring GraphsChapter 13.3 - Circuit Testing And Facilities DesignChapter 14 - The Max Flow - Min Cut TheoremChapter 14.1 - Flows And CutsChapter 14.2 - Constructing Maximal FlowsChapter 14.3 - ApplicationsChapter 14.4 - Matchings
Book Details
Far more "user friendly" than the vast majority of similar books, this text is truly written with the "beginning" reader in mind. The pace is tight, the style is light, and the text emphasizes theorem proving throughout. The authors emphasize "Active Reading," a skill vital to success in learning how to think mathematically (and write clean, error-free programs).
Sample Solutions for this Textbook
We offer sample solutions for Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series) homework problems. See examples below:
More Editions of This Book
Corresponding editions of this textbook are also available below:
Discrete Mathematics With Graph Theory With Discrete Math Workbook: Interactive Exercises (3rd Edition)
3rd Edition
ISBN: 9780132245883
Discrete Mathematics with Graph Theory
3rd Edition
ISBN: 9780131679955
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