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Appendix A Selected Hints
0 Introduction and Preliminaries
0 Introduction and Preliminaries
0.2 Mathematical Statements
Exercises
0.2.18.
0.2.19.
0.3 Sets
Exercises
0.3.7.
0.3.14.
0.3.17.
0.3.18.
0.3.29.
0.4 Functions
Exercises
0.4.20.
0.4.25.
0.4.29.
1 Counting
1 Counting
1.1 Additive and Multiplicative Principles
Exercises
1.1.9.
1.1.11.
1.1.13.
1.1.14.
1.2 Binomial Coefficients
Exercises
1.2.5.
1.2.7.
1.3 Combinations and Permutations
Exercises
1.3.4.
1.3.6.
1.3.8.
1.3.11.
1.4 Combinatorial Proofs
Exercises
1.4.3.
1.4.4.
1.4.6.
1.4.7.
1.4.8.
1.4.9.
1.4.13.
1.4.14.
1.6 Advanced Counting Using PIE
Exercises
1.6.4.
1.6.13.
1.7 Chapter Summary
Chapter Review
1.7.16.
2 Sequences
2 Sequences
2.1 Describing Sequences
Exercises
2.1.11.
2.1.12.
2.1.15.
2.1.16.
2.1.18.
2.1.19.
2.4 Solving Recurrence Relations
Exercises
2.4.3.
2.5 Induction
Exercises
2.5.9.
2.5.11.
2.5.15.
2.5.17.
2.5.18.
2.5.20.
2.5.21.
2.5.22.
2.5.23.
2.5.24.
2.5.26.
2.5.27.
2.5.29.
2.6 Chapter Summary
Chapter Review
2.6.14.
2.6.15.
2.6.16.
3 Symbolic Logic and Proofs
3 Symbolic Logic and Proofs
3.1 Propositional Logic
Exercises
3.1.4.
3.1.5.
3.1.10.
3.1.11.
3.1.15.
3.1.18.
3.1.19.
3.2 Proofs
Exercises
3.2.5.
3.2.6.
3.2.7.
3.2.9.
3.2.11.
3.2.13.
3.2.14.
3.2.15.
3.2.16.
3.2.18.
3.2.19.
4 Graph Theory
4 Graph Theory
4.1 Definitions
Exercises
4.1.3.
4.1.6.
4.1.7.
4.1.8.
4.1.11.
4.1.12.
4.1.13.
4.1.14.
4.1.15.
4.1.16.
4.2 Trees
Exercises
4.2.3.
4.2.4.
4.2.5.
4.2.7.
4.2.8.
4.2.9.
4.2.10.
4.2.14.
4.2.15.
4.2.16.
4.3 Planar Graphs
Exercises
4.3.3.
4.3.5.
4.3.11.
4.3.14.
4.3.15.
4.4 Coloring
Exercises
4.4.7.
4.4.10.
4.4.13.
4.4.14.
4.5 Euler Paths and Circuits
Exercises
4.5.7.
4.5.9.
4.5.10.
4.7 Chapter Summary
Chapter Review
4.7.23.
5 Additional Topics
5 Additional Topics
5.1 Generating Functions
Exercises
5.1.10.
5.2 Introduction to Number Theory
Exercises
5.2.13.
5.2.18.
