Math 109 Homework Assignments

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Math 109 Spring 2022
Homework Assignments

Updated 5/18/22

Homework Guidelines

Upload your homework to Gradescope according to the following guidelines.

Format Guidelines
- Turn in only those exercises enclosed in square brackets, for example [100].
- Use clean, white paper in order to make your solutions clearly legible.
- Start each problem on a new page.
- Write neatly (or type) and use complete sentences in your solutions.
Attribution Guidelines
- You may consult any book, periodical, website or person for assistance provided you give credit to your source.
- You must give credit to any book, periodical, website or person from which you obtained assistance.
  - Mary Jones told you the main idea for proof in problem 1.1. You would write something like: "Mary Smith told me the main idea for this proof."
  - You found the solution to problem 2.1 in "Naive Set Theory" by Paul Halmos. You would write something like: "I found this solution in _Naive_Set_Theory_ by Paul Halmos."
- There is no penalty for finding a solution in a book or getting it from a friend; however, failing to give appropriate credit would be considered an academic integrity violation. Please be honest and give credit to your sources. Your integrity will shine by doing this.
- It is, of course, to your benefit to discover and work out as many of the solutions for yourself as possible; however, you should feel free to discuss the problems and make use of available resources (making sure to give appropriate credit).

Homework 1

Turn in only those exercises enclosed in square brackets, e.g. [9].

Due Thursday, April 7 Exercises: 1.2, 1.5, 2.3, 2.5, 3.2, 3.7, 4.1, 4.7 Problems I (pg 53-57): 1, 2, [4], 5, [6], [10] For number 6, only the first equality in parts (i) and (ii) need be proven. For number 10, provide a brief yet clear explanation. Extra: [1.] Let a and b be integers and let d be a positive integer. Prove the following proposition: If d divides a and d divides b, then d divides both a + b and a - b. Is the converse of the proposition in (a) above true? If so, prove it; if not, exhibit a counterexample.

Homework 2

Turn in only those exercises enclosed in square brackets, e.g. [19].

Due Thursday, April 14 Exercises: 5.1, 5.6, 6.4, 6.6, 6.7 Problems I (pg 53-57): 11, [14], [19], [21], [25] Problems II (pg 115-119): 7, [8]

Midterm Exam 1 (Wednesday, April 20)

Homework 3

Turn in only those exercises enclosed in square brackets, e.g. [45].

Due Thursday, April 28 Exercises: 7.7, 9.5, 15.5, 15.6, 16.3, 16.4 Problems II (pg 115-119): [15], [19] Problems IV (pg 225-228): [1], [4], 6, [7], 8^*, 10