All Homework

Comments for all assignments

• Problems are taken from the textbook unless otherwise noted.
• For full credit, provide context for each problem, show all calculations, and justify all answers by providing enough comments to explain your reasoning.
• You will lose a significant amount of credit if you do not provide context, calculations, and justifications for a problem.
• Numbers and/or algebra by themselves are not enough. A correct answer with no justification will be worth no more than half credit, and sometimes much less than that.
• Precision is very important. You cannot skip steps, make guesses, or use flawed logic. Any of these things can lead to incorrect answers.
• Homework assignments must be very neatly written or typeset (e.g. using Word or OpenOffice).
• You must indicate any assistance/collaboration you had on an assignment as specified on the Policies page.

Homework 1

Answer the following questions based on the course website. For each one, give an answer and specify which link on the left you clicked to get the information. For instance, your answer for one might be:

      23. Certainly (Gradebook)

1. How often should you check your e-mail?
2. How many assignments can you turn in late?
3. At exactly what time are homework assignments due (be precise)?
4. If you come to class 10 minutes late with your homework, will I accept it?
5. What percentage of your grade are the exams? What percent is each exam?
6. When are my office hours?
7. If you get help from or work with others on an assignment, what do you need to do?
8. Does neatness/organization of homework matter at all?
9. Do you have to show all of your work on homework problems, whether or not the problem says so?
10. Can you tell exactly what grade you got on any assignment in the course at any time? Can you get an idea of how your grade compares with the grade of others?
11. If you talk about homework problems with others and are able to write down a solution but you don't fully understand it, should you include it on your homework assignment? Explain.
12. Will I give extra credit assignments to students who are not performing well in the course?
13. What is the reading assignment for Monday, January 21?
14. How many homework assignments are there currently scheduled?
15. What dates are you going to be in class taking an exam?
16. Are there any solutions available for the exercises in the book? If so, where?
17. What should you do after every homework assignment is handed back?
18. What is the earliest possible date and time you can leave Hope College at the end of the semester?
19. If you give or take answers from classmates, the Internet, etc., what will be the result?
20. How is learning like sports?

Homework 2

Section	Problem	Notes
1.1	18
	32e
	28a
	42
1.2	18	Give all of the possible combinations that work.
	36
	40b	Look at #41 to see what sort of answer it is looking for.

Homework 3

Section	Problem	Notes
1.3	10d	For this and similar problems: List the variable columns and rows in the same order as the examples in the textbook. Show intermediate columns as necessary. A truth table is not a proof. Clearly state why the truth table proves what is asked.
	14
	16	Read the paragraph before the problem.
	30	Begin by realizing that it can only be false if the premise is true but the conclusion is false. Then argue that if the conclusion is false, the premise is too.
1.4	14	Justify your answers by providing an example, counter example, and/or brief explanation.
	36
	50	Define a universe of discourse and choose statements P and Q on that universe such that the given statements have different truth values. Notice that 49 is similar.

Homework 4

Section	Problem	Notes
1.6	16bc	Clearly state whether or not the argument is correct and give the specific rule(s) of inference or fallacy used.
	20	Explain why or why not, specifying rules of inference/fallacies.
1.7	2	Be very precise, using the definition of even. You cannot not say, for instance, that 10x+14y-6z+12 is even. You must use algebra to make it look like 2k for some integer k. Similarly for future problems dealing with with either odd or even numbers. Also, a common mistake on this kind of proof is to write it in such a way that you are essentially assuming the two numbers are the same number without realizing it.
	18	Take the assumption that n is an integer as a given, and read the problem as "If 3n+2 is even, then n is even."
	24

Homework 5

Section	Problem	Notes
2.1	30	Prove your conclusion.
	36
2.2	12	Use a "set containment proof". See Examples 10 and 12. Your proof should contain phrases like "Let x∈FOO", "by the definition of union", "thus FOO⊆FERZLE", etc.
	16a	See note for the previous problem.
	52
	58	This is asking two separate questions—one about unions and the other about intersections. It is not asking about doing both at the same time since it is unclear what that would even mean.

Homework 6

Section	Problem	Notes
2.4	16b
	26b	Do not give a recursive formula. I should be able to determine a100 by just plugging in 100, for instance. Assume the first term is a1.
	32d
	40
2.6	4b	Show all of the intermediate calculations.
	10	Make sure to specify the size or tell why it is not defined.
	26	Write out the intermediate step(s)
	28	Write out the intermediate step(s)

Homework 7

Section	Problem
4.1	20
	30
	32ab
4.2	28
4.3	24bd
	28
	32e

Homework 8

Section	Problem	Comments
4.5	2ab	You can use a calculator for this one.
	6
	16
	24b
4.6	8	Also give the value of k that was used to encrypt the message. You should not use any tools besides a calculator to solve this. See Example 5 for one way to proceed.
	24	You may use whatever tools you wish to do the exponentiation. Wolfram Alpha is a good choice.

Homework 9

Section	Problem	Notes
5.1	6	Look at the solutions to similar problems (e.g. #5, #7)
	20	Don't make this one harder than it is. It is fairly straightforward.
	50
5.3	12	Recall that f0=0 and f1=1. This one should not be too difficult if you use the correct proof technique.
	18
	24a	The empty string (λ) is a palindrome.
	38

Homework 10

Section	Problem	Notes
6.1	12
	32	Do not make these ones harder than they are. Also, do not simplify your answers. For examples, 263 or 26*25*24 are acceptable.
	40
6.2	16
	36
	40	Don't use induction. There is a much easier way to think about it. (Hint: What section is this in?)

Homework 11

Section	Problem
6.3	22
	24
	30
6.4	4
	8
	28