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Chapter B Selected Solutions

Chapter 0 Introduction and Preliminaries

Section 0.2 Mathematical Statements

Subsection Exercises

0.2.1
0.2.4
0.2.5
0.2.6
0.2.7
0.2.9
0.2.12
0.2.14
0.2.15

Section 0.3 Sets

Subsection Exercises

0.3.1
0.3.2
0.3.3
0.3.4
0.3.5
0.3.6
0.3.7
0.3.8
0.3.9

Section 0.4 Functions

Subsection Exercises

0.4.1
0.4.2
0.4.5
0.4.9
0.4.10

Chapter 1 Counting

Section 1.1 Additive and Multiplicative Principles

Subsection Exercises

1.1.1
1.1.2
1.1.5
1.1.6
1.1.7
1.1.8
1.1.9
1.1.12

Section 1.2 Binomial Coefficients

Subsection Exercises

1.2.1
1.2.2
1.2.3
1.2.4
1.2.5
1.2.6
1.2.9
1.2.10
1.2.12

Section 1.3 Combinations and Permutations

Subsection Exercises

1.3.1
1.3.2
1.3.3
1.3.5
1.3.7
1.3.8
1.3.9
1.3.10
1.3.11
1.3.12
1.3.13

Section 1.4 Combinatorial Proofs

Subsection Exercises

Section 1.5 Stars and Bars

Subsection Exercises

1.5.1
1.5.2
1.5.4
1.5.5
1.5.6
1.5.7
1.5.8
1.5.10
1.5.11

Section 1.6 Advanced Counting Using PIE

Subsection Exercises

1.6.1
1.6.3
1.6.4
1.6.5
1.6.8
1.6.9
1.6.11
1.6.12
1.6.13

Section 1.7 Chapter Summary

Subsection Chapter Review

1.7.1
1.7.3
1.7.5
1.7.6
1.7.7
1.7.8
1.7.9
1.7.10
1.7.11
1.7.12
1.7.13
1.7.14
1.7.16
1.7.17
1.7.18
1.7.19

Chapter 2 Sequences

Section 2.1 Describing Sequences

Subsection Exercises

2.1.1

Section 2.2 Arithmetic and Geometric Sequences

Subsection Exercises

2.2.2
2.2.3
2.2.4
2.2.5
2.2.6
2.2.7
2.2.8
2.2.9

Section 2.3 Polynomial Fitting

Subsection Exercises

2.3.1
2.3.2
2.3.3
2.3.4
2.3.8

Section 2.4 Solving Recurrence Relations

Subsection Exercises

2.4.3
2.4.5
2.4.6
2.4.7

Section 2.5 Induction

Subsection Exercises

Section 2.6 Chapter Summary

Subsection Chapter Review

2.6.1
2.6.2
2.6.3
2.6.5
2.6.8
2.6.10
2.6.11

Chapter 3 Symbolic Logic and Proofs

Section 3.1 Propositional Logic

Subsection Exercises

Section 3.2 Proofs

Subsection Exercises

Section 3.3 Chapter Summary

Subsection Chapter Review

Chapter 4 Graph Theory

Section 4.1 Definitions

Subsection Exercises

Section 4.2 Trees

Subsection Exercises

Section 4.3 Planar Graphs

Subsection Exercises

Section 4.4 Coloring

Subsection Exercises

Section 4.5 Euler Paths and Circuits

Subsection Exercises

Section 4.6 Matching in Bipartite Graphs

Subsection Exercises

Section 4.7 Chapter Summary

Subsection Chapter Review

Chapter 5 Additional Topics

Section 5.1 Generating Functions

Subsection Exercises

Section 5.2 Introduction to Number Theory

Subsection Exercises