MATH 2602 Homework #1-#6
Due Wednesday Aug 21 - Sep 24, covering the material of Exam 1 on Sep 24

• Homework 1 - Due Aug 20 [Barone]
• Core : Book problems: Section 0.1 on page 8-10 problems 3b, 3c, 3g, 4(even letters only), 5b, 5j. Also, 
• A1: Write down the negation of the following statements. Do not write "it is not the case that" and be clear and concise in your answer.
• If we live at the same house, then we will take the same bus from school.
• Either the sum of three numbers is zero or one of the numbers is not zero.
• The sum of positive numbers is positive and zero is positive.
• A2: Write the implication in "if-then" form. Give an assignment of T=true or F=false to each of the supposition and conclusion of the implication
  and say whether the implication is true or false in this case. Now find an assignment of T or F which makes the implication the other truth-value
  (so that you have one assignment which makes the implication true and one that makes it false).
• We rode on the same bus because we live at the same house.
• I didn't break the law because I'm not childish and stupid.
• Supplementary: None this week. 

• Homework 2 - Due Aug 27 [Barone-Kim]
• Core : Book problems: Section 0.1 on page 9 problems 6b-6c, 6f, 6i, 7d, 7f, 7k.
  Section 0.2 on page 16 problems 3b, 3d, 3f, 6, 7, 13.
  Review Exercises for Chapter 0 on page 17-18 problems 2a, 3a, 15, 16.
  Section 1.1 on page 23 problems 1b, 2a, 4. 
• Supplementary
  1) Construct a truth table for the following compound statements and conclude whether or not they are logically equivalent
  
• p and (q or r)
• (p and q) or (p and r)

• Homework 3 - Due Sep 3 [Barone-Celaya]
• Core : Book problems: Section 1.1 on page 23 problems 6a, 9b, 10a.
  Section 1.2 on page 29-30 problems 2b, 3b, 4b, 7a, 10c, 10e.
  Section 1.3 on page 24 problem 1c-1f. 
• Supplementary
  Is the following argument valid?
  
• If I had my umbrella whenever it rained, then I didn't get wet.
• If it rained, then I had my umbrella and didn't get wet.
• If I didn't bring my umbrella, then I would get wet if it rained but remain dry otherwise.
• -----------------
• I brought my umbrella.

• Homework 4 - Due Sep 10 [Barone-Rybka]
• Core : Book problems: Section 1.3 on page 34-35 problems 3b, 4g, 5i, 5j.
  Review Exercises for Chapter 1 on page 36-37 problems 2, 3b, 3d, 5a, 8a.
  Section 5.1 on page 156-157 problems 3, 4d, 5a, 13. 
• A1: Prove using the strong form of mathematical induction that every positive integer greater than one is the product of finitely many primes.
• Supplementary: Find a formula for ½+¼+⅛+…+1⁄2ⁿ by examining the values of this expression for small values of n.
  Bonus problem (not graded): Use induction to show that n people can divide a cake (where each person gets one or more separate pieces of the cake) so that the cake is divided fairly. 

• Homework 5 - Due Sep 17 [Barone-McKay]
• Core : Book problems: Section 6.1 on page 190-192 problems 1c, 1d, 3a, 3d, 10b.
  Section 6.2 on page 198-199 problems 4a, 4b, 6a, 8a-8d, 12, 17a-17d.
  Section 6.3 on page 202-203 problems 2, 6(do the n=5 case first), 8a, 8b.
  Review exercises for Chapter 6 problem 3b. 
• Supplementary: Assume that if person A knows person B, then person B knows person A. Prove that, in any group of six people, you can always
  find three people that all know each other or three people such that none of them know each other.
  (So, a group of people A, B, and C such that A, B, and C each know each other or A does not know B, A does not know C, and B does not know C).  

• Homework 6 - Due Sep 24 [Barone-Kim]
• Core : Book problems: Section 7.1 on page 209-210 problems 2, 4, 6, 7a, 7b, 11
  Section 7.2 on page 215-216 problems 2a, 2b, 4, 9, 11.
  
• Supplementary: TBD. 

• Exam 1 Wednesday Sep 24 will cover material from Hw/Quiz 1-6: essentially Chapter 0 - Chapter 1 of the textbook, Section 5.1 on mathematical induction, the first three sections
  of Chapter 6 on basic counting principles, and the first two sections of Chapter 7 on combinations and permutations.