## Homework

NOTICE: You must show all of your work to receive full marks. As well, I have given the marker permission to dock marks if your assignment is not neat, orderly, and stapled.

Assignment #1, due September 14th SOLUTIONS

• §1: 1.2, 1.4, 1.8, 1.16, 1.20. 1.24, 1.30
Assignment #2, due September 21st SOLUTIONS
• §2: 2.2, 2.4, 2.6, 2.8, 2.10, 2.12, 2.14, 2.18, 2.20, 2.24, 2.28, 2.32
Assignment #3, due September 28th SOLUTIONS
• §2: 2.34, 2.38, 2.40, 2.42, 2.46, 2.68
• § 3: 3.4, 3.6, 3.8, 3.12
• Let S = [1,2] and let T = (3, ∞). Describe the truth values of each of the following statements. Explain your answer carefully -- no explanation, no marks.
• ∃ x ∈S s.t. ∃ y ∈T s.t. |x-y|>3
• ∃ x ∈S s.t. ∀ y ∈T, |x-y|>3
• ∀ x ∈S, ∃ y ∈T s.t. |x-y|>3
• ∀ x ∈S, ∀ y ∈T, |x-y|>3
Assignment #4, due October 12th SOLUTIONS
• §3: 3.14, 3.16, 3.20, 3.22, 3.24
• §4: 4.2, 4.4, 4.10, 4.14, 4.16
Assignment #5, due October 19th SOLUTIONS
• §4: 4.18, 4.20, 4.30, 4.32, 4.36, 4.46
• §5: 5.4, 5.6
Assignment #6, due October 26th SOLUTIONS
• §5: 5.16, 5.20, 5.28, 5.36, 5.48
• §6: 6.1, 6.6 (hint: recall the story of Gauss on page 133), 6.14
Assignment #7, due November 2nd SOLUTIONS
• §6: 6.22, 6.40
• §8: 8.4, 8.12, 8.20
• §9: 9.2, 9.10, 9.12, 9.24
Assignment #8, due November 16th SOLUTIONS
• §9: 9.28, 9.32
• §10: 10.4, 10.12, 10.16, 10.18, 10.22
Assignment #9, due November 23rd SOLUTIONS
• §10: 10.24, 10.26, 10.32, 10.33
• Prove that the function f:NxN ---> N defined by f(a,b)=2a3b is an injection.
• §12: 12.2, 12.4, 12.6