# Problem Set Assignments

Fall 2019

Here is a running schedule of the problems that are assigned for as our problem sets throughout the term. Remember that the problem set exercises are not the upper limit of the problems you should do: The more exercises from the book you try, the better off you will be.

Unless otherwise noted, problem sets are always due by 5 p.m. on the due date. Each PS is worth 30 points. Each individual problem is worth 6 points unless otherwise indicated.

If an assignment has a written-out portion, you may either (a) bring it to class on the day it’s due, (b) slip it under Mark’s office door before it’s due, or (c) send it in an e-mail it to Mark before it is due. Whenever you submit a written portion of a problem set via email, please make sure to write “Written Portion: PS #” in the subject line, letting us know that your e-mail contains a written portion to be graded and telling us which problem set number it is for.

Hints and Solutions for some of these exercises are available under the “Hints & Solutions” section of the LPL web site after you have registered and logged in to that web site.

### Substitute Problems for the Argument Analysis Paper

These are an optional substitute for the 30 point Argument Analysis Paper.

Due: by 5 p.m. on Monday, December 9.

These are not part of the usual problem set schedule; they are not required. However, if you wish, you may submit these problems instead of the Argument Analysis assignment paper. This score will not drop out if it is your lowest “problem set” score, and it will not be accepted late.

There are four exercises from the textbook and one handout:

### Problem Set 7

Due: Friday, December 6 by 5 p.m.

• 13.23
• 13.26
• 13.30
• 13.33
• 13.52

Proofs and/or Counterexamples! Start early! Use the proof rule sheet and the strategy points laid out in Handout 15 if you get stuck. Remember that you can use the Taut Con rule in these proofs.

### Problem Set 6

Due: Monday, November 25 by 5 p.m.

• 11.16
• 11.17
• 11.20 (worth 9 points)
• 11.40 (worth 9 points)

Start early! Even though it involves translations rather than proofs, this might be the hardest problem set of the semester. Students in previous years have been especially emphatic about the difficulty of Exercises 11.20 and 11.40.

Check your work with the Grade Grinder regularly, after every few sentences you attempt, rather than waiting until the end. Don’t make the mistake of thinking that just because your sentences are true in the specified world they must be correct.

Hints are available at the LPL website for parts of 11.17, 11.20, and 11.40.

Here is one more hint of my own for Exercise 11.20, Sentence 12. Notice that one of the things that is smaller than something that is larger than b will be b itself. The Grade Grinder expects you to understand that fact and assume it as you do your translation. Otherwise, your translation will “time out.”

### Problem Set 5

Due: Wednesday, 11/06 by 5 p.m.

• 9.3
• 9.9
• 9.12
• 9.16
• 9.17

A “wff” is a “well-formed formula”: a piece of our FOL language that is grammatically put together. Anything that is a sentence of FOL is going to be a well-formed formulae. But so are grammatical formulae that have unquantified variables, like “Cube(x)” or “Larger(y,b).”

Remember that checking your translations against sample worlds is helpful, but it does not guarantee that your translations are correct. Make sure to use the “just me” option in the grade grinder early and often to check your translations as you work.

You don’t have to wait until you’re done with all of the translations before you check your work in the grade grinder. If you want to check, say, the first four sentences you’ve written, you can do that; the grade grinder will report that your blank sentences are incorrect, but who cares? “Just me” submissions don’t count for a grade.

Hints are available at the LPL website for some of these problems.

### Problem Set 4

Due: on Wednesday, Oct. 23 Friday, Oct. 25 by 5 p.m.

• 7.12
• 7.15
• 8.25
• 8.32
• 8.35

The problems from Chapter 8 involve proofs, so start working early! Don’t forget to run your translations for 7.12 and 7.15 through the Grade Grinder before you submit them for credit.

### Problem Set 3

Due: Wednesday, October 2

• 6.14
• 6.25 (don’t worry about doing the “informal proof”)
• 6.31
• 6.32
• 6.35

Make sure to read the instructions for each problem; some of them will ask you first to determine whether the argument is valid or invalid and then complete the exercise accordingly. (It is never fun to spend several hours trying to construct a proof of an argument only to find out that it is invalid and no proof is available.)

Start early! Proofs are hard, and you’re more likely to get stuck and need help with these problems than with the earlier problem sets.

My advice from the syllabus is especially apt when it comes to proofs: Treat the problem set as the bare minimum group of problems, and go on to do as many other exercises from the book as you can stand.

When you receive your official “Instructor Too” report for PS 3, the Grade Grinder will say some things that might worry you, but which are not really a problem:

• For exercises where you are not told in advance whether the argument is valid or invalid, it will tell you exactly what you did and did not submit. So, for instance, if you submit a proof for a valid argument, it will still tell you that you did not submit a world file. But that is not a problem: you shouldn’t be submitting a world for valid arguments. (The same thing goes in reverse for invalid arguments: it will tell you that you didn’t submit a proof, but that’s okay.)
• Also, Grade Grinder will tell you how many steps beyond the premises were in any proof you submitted. There is no need to worry about this, either.
• For EXERCISE 6.25, GG will say

???? We did not receive your written work. We hope you turned it in to your instructor.

That is referring to the informal proof that you did not have to do. So, again, no need to worry.

### Problem Set 2

Due: Monday, September 23, by 5 p.m.

• 4.6
• 4.8 (use Handout 6, please)
• 4.17
• 4.22
• 4.23

For Exercise 4.8, use worksheet from Handout 6, whiich has the Euler diagram already drawn on it.

### Problem Set 1

Due: Friday, September 13 by 5 p.m.

Note that this is a very late due date for this problem set; it is due in the third week of the semester. You can and should start working on this problem set earlier than this date would suggest.

Note: Problem 3.10 asks you to submit both files when you’re done. It’s asking for the world file that you modified and renamed as “World 3.10.wld”, and it also wants you to submit the sentence file. The Grade Grinder will complain if you do not submit the sentences, but I don’t care whether you do so or not, and you will not lose points for not submitting them. I am confident you can type.

If you get stuck on 3.14 or 3.21, you can find some help in the “Hints” file for Chapter 3 from the LPL web site. (You will need to have purchased/registered the software before you can log in on the page and see the hints.) Also, note that Exercise 3.22, which is not assigned, can help you check your answers to Exercise 3.21.