DISCRETE MATHEMATICS & ITS APPLICATIONS SOLUTIONS GUIDE - COMPLETE 8TH EDITION - STEP-BY-STEP ANSWERS TO ALL EXERCISES

All Chapters Covered
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SOLUTION MANUAL
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, Contents
Preface iii

CHAPTER m m 1 Them Foundations:m m Logicm andm Proofs 1
1.1 Propositional m Logic 1
1.2 Applicationsm ofmPropositionalm Logic 8
1.3 Propositional m Equivalences 11
1.4 Predicatesm andm Quantifiers 17
1.5 Nestedm Quantifiers 23
1.6 Rulesm ofm Inference 32
1.7 Introductionm tom Proofs 36
1.8 ProofmMethodsm andm Strategy 40
Guidem tom Reviewm Questionsm form Chapterm 1 44
Supplementarym Exercisesm form Chapterm 1 45
Writingm Projectsm form Chapterm m 1 48

CHAPTER2 Basicm Structures:m Sets,m Functions,
Sequences,m Sums,m andm Matrices 50
2.1 Sets 50
2.2 Setm Operations 53
2.3 Functions 59
2.4 Sequencesm andm Summations 68
2.5 Cardinalitym ofm Sets 75
2.6 Matrices 79
Guidem tom Reviewm Questionsm form Chapterm 2 83
Supplementarym Exorcisesm form Chapterm 2 84
Writingm Projectsm form Chapterm 2 87

CHAPTERm 3 Algorithms 88
3.1 Algorithms 88
3.2 ThemGrowthmofmFunctions 97
3.3 Complexitym ofmAlgorithms 103
GuidemtomReviewmQuestionsmformChapter 107
m3mSupplementarym ExercisesmfrmChapte 108
rm 3mWritingmProjectsmformChapterm3112

CHAPTERm 4 Numberm Theorym andm Cryptography 113
4.1 DivisibilitymandmModularmArithmetic 113
4.2 IntegermRepresentationsmandmAlgorithm 116
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4.3 Primesm andm Greatestm Commonm Divisor 122
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4.4 Solvingm Congruences 130
4.5 Applications m ofm Congruences
GuidemtomReviewmQuestionsmformChapterm137 142
44.6 Cryptography 140
mSupplementarym ExercisesmformChapterm 143
4mWritingmProjectsmformChapterm4 147

V

,CHAPTERm5 Inductionm andm Recursion 149
5.1 Mathematicalm Induction 149
5.2 Strongm Inductionm andm Well-Ordering 161
5.3 RecursivemDefinitionsmandmStructuralmInductio 167
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5.4 Recursivem Algorithms 176
5.5 Program m Correctness 182
GuidemtomReviewmQuestionsmformChapter 183
m5mSupplementarymExercisesmformChapte 185
rm5mWritingmProjectsmformChapterm5195

CHAPTERm 6 Counting 197
6.1 ThemBasicsmofmComuting 197
6.2 Them Pigeonholem Principle 206
6.3 Permutationsm andm Combinations 211
6.4 Binomialm Coefficientsm andm Identities 216
6.5 Generalizedm Permutationsm andm Combinations 220
6.6 GeneratingmPermutationsmandmCombinations 227
Guidem tom Reviewm Questionsm form Chapterm 6 230
Supplementarym Exercisesm form Chapterm 6 231
Writingm Projectsm form Chapterm 6 237

CHAPTERm 7 Discretem Probability 239
7.1 AnmIntroductionm tomDiscretemProbability 239
7.2 Probabilitym Theory 242
7.3 Bayes'm Theorem 247
7.4 Expectedm Valuem andm Variance 250
Guidem tom Reviewm Questionsm form Chapterm 7 255
Supplementarym Exercisesm form Chapterm 7 256
Writingm Projectsm form Chapterm 7 261

CHAPTERm 8 Advancedm Countingm Techniques 262
8.1 Applicationsm ofm Recurrencem Relations 262
8.2 Solvingm Linearm Recurrencem Relations 272
8.3 Divide-and- 282
ConquermAlgorithmsm andmRecurrencemRelations
8.4 Generatingm Functions 286
8.5 Inclnsion-Exclusion 298
8.6 Applicationsm ofm Inclusion-Exclusion 300
GuidemtomReviewmQuestionsmformChapterm8 304
Supplementarym m Exercisesm form Chapterm 8 305
Writingm Projectsm form Chapterm 8 310

CHAPTERm Relations v
9 9.1 Relationsm andm Theirm Properties 312
9.2 n- 320
9.3 arymRelationsm andmTheirmApplications
9.4 Representingm Relations 322
ClosuresmofmRelations 325

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