Problem Selection

Chapter 1: Sentential Logic

1.1 Deductive Reasoning and Logical Connectives

1 F
5 F
7 F

1.2 Truth Tables

1 F
3 F
4 F
8ab F
9a F
10 F
11 F
12 F
13 F
16 F
18 F

1.3 Variables and Sets

4 F
5 F
7 F
9 F

1.4 Operations on Sets

1 F
4 F
5 F
10 F
13 F

1.5 The Conditional and Biconditional Connectives

1 F
6 F
7 F
9 F
11 F

Chapter 2:Quantificational Logic

2.1 Quantifiers

3 F
5 F
7 F
8 F
9 F
10 F

2.2 Equivalence Involving Quantifiers

1 F
3 F
4 F
5 F
6 F
7 F
8 F
9 F
10 F
14 F
15 F

2.3 More Operations on Sets

1 F
3 F
8 F
12 F
13 F
15 F

Chapter 3: Proofs

3.1 Proof Strategies

1 F
3 F
5 F
8 F
14 F
15 F
16 F
17 F

3.2. Proofs Involving Negations and Conditionals

1 F
2 F
5 F
6 F
11 F
12 F
13 F

3.3 Proofs Involving Quantifiers

1 F
2 F
5 F
7 F
15 F
18 F
19 F
20 F
21 F
22 F
23 F
24 F

3.4 Proofs Involving Conjunctions and Biconditionals

1 F
2 F
8 F
10 F
11 F
12 F
26 F
27 F

3.5 Proofs Involving Disjunctions

1 F
5 F
8 F
10 F
13 F
27 F
28 F
29 F
31 F

3.6 Existence and Uniqueness Proofs

1 F
6 F
10 F
13 F

3.7 More Examples of Proofs

6 F
10 F

Chapter 4: Relations

4.1 Ordered Pairs and Cartesian Products

3 F
5 F
6 F
7 F (no need to prove)
8 F
12 F
13 F
15 F

4.2 Relations

5 F
7 F
9 F
10 F
11 F
12 F
13 F

4.3 More about Relations

3 F
4 F
7 F
8 F
9 F
10 F
11 F
12 F
13 F
17 F
19 F
22 F
24 F

4.4 Ordering Relations

1 F
3 F
4 F
6 F
14 F
17 F
19 F
23 F

4.5 Equivalence Relations

1 F
2 F
8 F
11 F
12 F
13 F
14 F

Chapter 5: Functions

5.1 Functions

1(a)(b) F
3 F
7(a)(b) F
8 F
9 F
12 F
20 F
21 F

5.2: One-to-One and Onto

5 F
6 F
7 F
10 F
11 F
13 F

5.3: Inverses of Functions

3 F
8 F
9 F
11 F
18 F

5.4: Closures

1 F
5 F
11 F
12 F

5.5: Images and Inverse Images: A Research Project

1 F
2 F
3 F
4 F
5 F
6 F
7 F

Chapter 6 Mathematical Induction

Proof by Mathematical Induction

1 F
4 F
7 F
9.(a) F
15 F
16 F
19 F
20 F

6.2 More Examples

6 F
17 F
18 F

6.3 Recursion

1 F
5 F
7 F
16 F
18 F
19 F

6.4 Strong Induction

2 F
3 F
11 F

6.5 Closures again

1 F
2 F
4 F

Chapter 7: Number Theory

7.1 Greatest common Divisors

2(a) F
5 F
7 F
11 F
12 F

7.2: Prime Factorization

4 F
5 F
6 F
9 F
11 F
13 F

7.3: Modular Arithmetic

1 F
2 F
3 F
4 F
5 F
6 F
7 F
8 F
10 F
17 F
18 F
19 F
20(b) F

7.4: Euler’s Theorem

1 F
2 F
5 F
6 F
7 F
10 F
11 F
15 F

7.5: Public-Key Cryptography

4 F
6 F
7 F

Chapter 8: Infinite Sets

8.1 Equinumerous Sets

1 F
2 F
3(a)(b)(c) F
6 F
7 F
8 F
9 F
10 F
11 F
14 F
15 F
17 F
21 F
22(a) F
23(a)(b)(c) F
24(a)(b) F
26 F

8.2: Countable and Uncountable Sets

1 F
3 F
4 F
5 F
6 F
12 F

8.3: The Cantor-Schroder-Bernstein Theorem

1 F
2 F
3 F
4 F
5 F
6 F
7 F
12(b) F (note: don’t use (a) but use that R ~ {yes, no}^N and apply properties)
14(a)(b) F (note: similar as above, use properties you know, not an explicit bijection)