# Discrete Mathematics with Applications, 7th Edition Discrete Mathematics with Applications, 7th ...

ISBN: 9780073383095 / 0073383090

### Chapter 1

The Foundations: Logic And Proofs

 1.1 Propositional Logic Exercises p.12 1.2 Applications of Propositional Logic Exercises p.22 1.3 Propositional Equivalences Exercises p.34 1.4 Predicates and Quantifiers Exercises p.53 1.5 Nested Quantifiers Exercises p.64 1.6 Rules of Inference Exercises p.78 1.7 Introduction to Proofs Exercises p.91 1.8 Proof Methods and Strategy Exercises p.108 Review Questions p.111 Supplementary Exercises p.111

### Chapter 2

Basic Structures: Sets, Functions, Sequences, Sums, And ...

 2.1 Sets Exercises p.125 2.2 Set Operations Exercises p.136 2.3 Functions Exercises p.152 2.4 Sequences and Summations Exercises p.167 2.5 Cardinality of Sets Exercises p.176 2.6 Matrices Exercises p.183 Review Questions p.186 Supplementary Exercises p.187

### Chapter 3

Algorithms

 3.1 Algorithms Exercises p.202 3.2 The Growth of Functions Exercises p.216 3.3 Complexity of Algorithms Exercises p.229 Review Questions p.232 Supplementary Exercises p.233

### Chapter 4

Number Theory And Cryptography

 4.1 Divisibility and Modular Arithmetic Exercises p.244 4.2 Integer Representations and Algorithms Exercises p.255 4.3 Primes and Greatest Common Divisors Exercises p.272 4.4 Solving Congruences Exercises p.284 4.5 Applications of Congruences Exercises p.292 4.6 Cryptography Exercises p.304 Review Questions p.307 Supplementary Exercises p.307

### Chapter 5

Induction And Recursion

 5.1 Mathematical Induction Exercises p.329 5.2 Strong Induction and Well-Ordering Exercises p.341 5.3 Recursive Definitions and Structural Induction Exercises p.357 5.4 Recursive Algorithms Exercises p.370 5.5 Program Correctness Exercises p.377 Review Questions p.378 Supplementary Exercises p.379

### Chapter 6

Counting

 6.1 The Basics of Counting Exercises p.396 6.2 The Pigeonhole Principle Exercises p.405 6.3 Permutations and Combinations Exercises p.413 6.4 Binomial Coefficients and Identities Exercises p.421 6.5 Generalized Permutations and Combinations Exercises p.432 6.6 Generating Permutations and Combinations Exercises p.438 Review Questions p.439 Supplementary Exercises p.440

### Chapter 7

Discrete Probability

 7.1 An Introduction to Discrete Probability Exercises p.451 7.2 Probability Theory Exercises p.466 7.3 Bayes' Theorem Exercises p.475 7.4 Expected Value and Variance Exercises p.492 Review Questions p.495 Supplementary Exercises p.496

### Chapter 8

 8.1 Applications of Recurrence Relations Exercises p.510 8.2 Solving Linear Recurrence Relations Exercises p.524 8.3 Divide-and-Conquer Algorithms and Recurrence Relations Exercises p.535 8.4 Generating Functions Exercises p.549 8.5 Inclusion-Exclusion Exercises p.557 8.6 Applications of Inclusion-Exclusion Exercises p.564 Review Questions p.566 Supplementary Exercises p.567

### Chapter 9

Relations

 9.1 Relations and Their Properties Exercises p.581 9.2 n-ary Relations and Their Applications Exercises p.589 9.3 Representing Relations Exercises p.596 9.4 Closures of Relations Exercises p.606 9.5 Equivalence Relations Exercises p.615 9.6 Partial Orderings Exercises p.630 Review Questions p.634 Supplementary Exercises p.635

### Chapter 10

Graphs

 10.1 Graphs and Graph Models Exercises p.649 10.2 Graph Terminology and Special Types of Graphs Exercises p.665 10.3 Representing Graphs and Graph Isomorphism Exercises p.675 10.4 Connectivity Exercises p.689 10.5 Euler and Hamilton Paths Exercises p.703 10.6 Shortest-Path Problems Exercises p.716 10.7 Planar Graphs Exercises p.725 10.8 Graph Coloring Exercises p.732 Review Questions p.737 Supplementary Exercises p.738

### Chapter 11

Trees

 11.1 Introduction to Trees Exercises p.755 11.2 Applications of Trees Exercises p.769 11.3 Tree Traversal Exercises p.783 11.4 Spanning Trees Exercises p.795 11.5 Minimum Spanning Trees Exercises p.802 Review Questions p.804 Supplementary Exercises p.805

### Chapter 12

Boolean Algebra

 12.1 Boolean Functions Exercises p.818 12.2 Representing Boolean Functions Exercises p.822 12.3 Logic Gates Exercises p.827 12.4 Minimization of Circuits Exercises p.841 Review Questions p.844 Supplementary Exercises p.844

### Chapter 13

Modeling Computation

 13.1 Languages and Grammar Exercises p.856 13.2 Finite-State Machines with Output Exercises p.863 13.3 Finite-State Machines with No Output Exercises p.875 13.4 Language Recognition Exercises p.887 13.5 Turing Machines Exercises p.897 Review Questions p.900 Supplementary Exercises p.901

### Chapter A

Appendix

 A3 Pseudocode Exercises p.A-16 A2 Exponential and Logarithmic Functions Exercises p.A-9 A1 Axioms for the Real Numbers and the Positive Integers Exercises p.A-6
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