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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.
Examples:
- 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).

#### 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.

#### 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) **

#### 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

#### Turn in only those exercises enclosed in square brackets, e.g. [12].

`
Due Thursday, May 5
`
**Exercises:** 17.1, 17.3, 17.6, 19.1, 19.4, 19.5
**Problems V (pg 271-273):** [1], [4], [6], 7, [8]

**Midterm Exam 2 (Wednesday, May 11) covers Chapters 1 - 9, 15 - 17, and 19 - 21, with an emphasis on Chapters 15 - 17 and 19 - 21.**

#### Turn in only those exercises enclosed in square brackets, e.g. [12].

`
Due Thursday, May 19
`

#### Turn in only those exercises enclosed in square brackets, e.g. [12].

`
Due Thursday, May 26
`
**Exercises:** 10.2, 10.3, 11.2, 11.6, 12.3, 12.5
**Problems III (pg 182-183):** 1, 2, [6], [7], [11], 12, [14], 17, [18], [20]

#### Practice for the final examination; not to be turned in.

`
Due Thursday, June 2
`

**The Final Examination (8:00am - 11:00am Friday, June 10) is cumulative**

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