CMSC203 Discrete Structures, Sections 0201, Fall 2006

Homework Assignments

Homework 1, Due Thursday 09/07

Homework 2, Due Thursday 09/14

1. Section 1.1 Exercise 16, parts a-g  (page 17).
   
   
2. Section 1.1 Exercise 60, parts a & b  (page 20). Show your reasoning.
   
   
3. Section 1.2 Exercise 8, parts b & c  (page 26).
   
   
4. Section 1.3 Exercise 10, parts a-e  (page 40).

Homework 3, Due Thursday 09/21

1. Section 1.5 Exercise 20, parts a-c  (page 75).
   
   
2. Section 1.5 Exercise 32  (page 75).
   
   
3. Section 1.5 Exercise 42  (page 75).
   
   
4. Section 1.5 Exercise 56  (page 76).

Homework 4, Due Thursday 09/28

1. Section 1.5 Exercise 50  (page 76).
   
   
2. Section 1.7 Exercise 14, parts c, d & e  (page 95).
   Note: To prove that X ⊆ Y, show that z ∈ X implies that z ∈ Y.
   To prove that X = Y, show that X ⊆ Y and Y ⊆ X.
   
   
3. Section 1.7 Exercise 18  (page 95).
   Note: To prove that X = Y, show that X ⊆ Y and Y ⊆ X.
   
   
4. Section 1.8 Exercise 26  (page 109).

Homework 5, Due Thursday 10/05

1. Section 2.2 Exercise 12  (page 142).
   
   
2. Section 2.2 Exercise 24, parts a, d & e  (page 143).
   
   
3. Section 3.3 Exercise 8  (page 253).
   
   
4. Section 3.3 Exercise 10  (page 253).

Homework 6, Due Thursday 10/12

1. Section 3.3 Exercise 34  (page 254).
   
   
2. Section 3.3 Exercise 52  (page 255).
   
   
3. Section 3.4 Exercise 12  (page 271).
   
   
4. Section 3.4 Exercise 44  (page 272).

Homework 7, Due Thursday 10/19

1. Section 3.3 Exercise 20  (page 254).
   
   
2. Section 3.4 Exercise 26, part c  (page 271-272).
   Note: the notation "5 | a + b" means "5 divides (a + b)", that is, (a + b) is a multiple of 5 or, if you prefer C syntax, "(a + b) % 5 == 0".
   
   
3. Chapter 3, Supplementary Exercise 40, parts a & b  (page 293-294).
   Hint: Prove there is a contradiction if p ≤ p'.
   
   
4. Section 8.2 Exercise 42  (page 556).

Homework 8, Due Thursday 10/26

1. Section 8.3 Exercises 34, 36 and 38  (page 565).
   
   
2. Section 8.4 Exercise 12, parts a, b & c  (page 575).
   
   
3. Section 8.4 Exercise 14  (page 576).
   
   
4. Section 8.4 Exercise 32  (page 577).
   Note: The definition of "vertex basis" is given just above Exercise 32. It will be helpful to translate this definition into mathematical notation. The point of assigning this exercise is for you to practice working with a new definition.

Homework 9, Due Thursday 11/02

1. Section 8.4 Exercise 20  (page 576).
   Hint: use proof by induction.
   
   
2. Section 8.5 Exercises 2, 4 6 and 8,  (pages 588-589).
   
   
3. Section 8.5 Exercise 28, parts a & b,  (page 590).
   
   
4. Section 8.5 Exercises 30, 32 and 34,  (page 590).

Homework 10, Due Thursday 11/16

1. Section 4.1 Exercise 28 parts a-f  (page 311).
   
   
2. Section 4.1 Exercise 38 parts a-c  (page 312).
   
   
3. Section 4.2 Exercise 14 parts a & b  (page 319).
   
   
4. Section 4.3 Exercise 24  (page 325).

Homework 11, Due Tuesday 11/28

1. Section 4.3 Exercise 26 parts a-c  (page 325).
   
   
2. Section 4.5 Exercise 10 parts a-f  (page 342).
   
   
3. Section 4.5 Exercise 46  (page 343).
   
   
4. Section 5.1 Exercise 32  (page 361).

Homework 12, Due Tuesday 12/05

1. Section 5.1 Exercise 18  (page 361).
   
   
2. Section 5.2 Exercise 38  (page 378).
   
   
3. Section 5.3 Exercise 10  (page 392).
   
   
4. Section 7.1 Exercise 6  (page 480).

Homework 13, Due Tuesday 12/12

1. Section 7.5 Exercise 2, parts a-e  (page 513).
   
   
2. Section 7.5 Exercise 40  (page 515).
   
   
3. Section 7.6 Exercise 28 parts a-h  (page 529). Instruction: You must first draw a Hasse diagram for this poset.
   
   
4. Section 2.6 Exercise 18  (page 195). Instruction: Show your work using the Chinese Remainder Theorem (i.e., guessing the answer doesn't count).