Sections, concepts, and problems

3.1. Methods of proof. Various rules of inference, validity vs. truth, some logical fallacies, direct proof, indirect proof, proof by contradiction, constructive and nonconstructive existence proofs, counterexamples, etc.
1, 3, 7e, 11bcd, 13, 17, 23, 29, 35, 51 [prove (i) -> (ii) -> (iii) -> (iv) -> (i); it then follows they are all equivalent]

3.2. Mathematical induction. The First and Second Principles of Mathematical Induction, the Well-Ordering Principle (sometimes called the Least Natural Number Principle).
1, 2, 3, 5, 13, 29, 39

3.3. Recursive definitions. How to define certain quantities by specifying base case(s) and a recursion relation.
1c, 3d, 5, 11, 21, 23c, 29, 33, 47b

Other Chapters

Chapter 1 | Chapter 2 | Chapter 3 | Chapter 4 | Chapter 6