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Solutions A Selected Hints

Chapter 0 Introduction and Preliminaries

Section 0.2 Mathematical Statements

Exercises Exercises

Section 0.3 Sets

Exercises Exercises

Section 0.4 Functions

Exercises Exercises

Chapter 1 Counting

Section 1.1 Additive and Multiplicative Principles

Exercises Exercises

Section 1.2 Binomial Coefficients

Exercises Exercises

Section 1.3 Combinations and Permutations

Exercises Exercises

Section 1.4 Combinatorial Proofs

Exercises Exercises

Section 1.6 Advanced Counting Using PIE

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Section 1.7 Chapter Summary

Exercises Chapter Review

Chapter 2 Sequences

Section 2.1 Describing Sequences

Exercises Exercises

Section 2.4 Solving Recurrence Relations

Exercises Exercises

Section 2.5 Induction

Exercises Exercises

Section 2.6 Chapter Summary

Exercises Chapter Review

Chapter 3 Symbolic Logic and Proofs

Section 3.1 Propositional Logic

Exercises Exercises

Section 3.2 Proofs

Exercises Exercises

Chapter 4 Graph Theory

Section 4.1 Definitions

Exercises Exercises

Section 4.2 Trees

Exercises Exercises

Section 4.3 Planar Graphs

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Section 4.4 Coloring

Exercises Exercises

Section 4.5 Euler Paths and Circuits

Exercises Exercises

Section 4.7 Chapter Summary

Exercises Chapter Review

Chapter 5 Additional Topics

Section 5.1 Generating Functions

Exercises Exercises

Section 5.2 Introduction to Number Theory

Exercises Exercises