The PDF version of the syllabus also contains the problem sets.
It is a requirement of the class that all of the problem sets must be completed and submitted for marking. (We'll let you off once, if you do miss one, but you will get no credit for that problem set.) Failure to submit all (but one) of the problem sets will automatically lead to a grade of NC. Please note that the requirement is that the problem sets should be "completed", and by that I mean that one has given them a proper effort. Simply turning in a piece of paper with a few random jottings does not count as completing a problem set.
As with any mathematical subject-matter, it is impossible to learn this material without doing a lot of exercises. The book contains many more exercises than are assigned, and students are encouraged to do additional exercises to improve their understanding of the material. Students should feel free to show any additional problems (or even assigned problems) that they have done to one of the instructors so as to get feedback on how they are doing.
Students are also encouraged to work on the problems together—though, of course, submitted material should be a student's own work.
Problem set grades are not a major component of the overall grade for the course and should not be regarded as such. The 'grades' for problem sets are primarily intended to give students a sense for how well they have understood the material in that unit. To that end, problem sets are graded on a scale of 1-5, with the different scores having the following meanings:
To re-emphasize, then: A score of "3" on a problem set is meant to indicate that a student has successfully mastered that material and is prepared for what it is to follow in the course. While there is no easy 'map' from problem set scores to letter grades, someone who is routinely getting 3's on the problem sets can fully expect to get at least a B on exams covering that same material (and so to get at least a B for the course). Remember, too, that effort matters a lot to us, so if you are not doing so well, there are lots and lots of opportunities to get help.
Do not compare problem set scores across graders. Different graders always have slightly different standards, and there is not really anything to do about that other than to take it into account. Which we will.
Section IA (pp. 253-5): 1a,c,d; 2, 3; 4a,c,g,h,j
You should submit problem 1(d), but it will not affect your grade.
What we'd like you to do is to think this through and try to find
a sentence that is true if 1(d) is false, and false if 1(d) is true.
Whatever your answer, please explain why you think it is correct.
Section IB (pp. 255-60): 1a; 2a,c; 3a,e; 4b,f; 6; 7a
Note: Problems 13 and 14 not assigned. But they are examples of the sorts of 'logic puzzles' that are found on the LSAT. They can be done by schematizing the various assertions and doing a truth-table, but it is probably easier just to think through them. There's also a Book of Logic Puzzles you might enjoy, written by Nicole Fegan (class of 2020).
Section IC (pp. 260-4): 1; 2; 5; 6; Extra Problems 1-2
NOTE: The Extra Problems are NOT optional. They are just problems that are not in the book.
Both Problem 6 and Extra Problem 1 are quite difficult to do completely correctly. Real proofs would use mathematical induction, and we do not expect anyone to give such a proof. (If you do, the induction is on the number of connectives in the statement.) It's enough to do the following. Consider some examples, and see if you can find a relevant pattern. Then just tell us what the pattern is and why the presence of that pattern makes the statements made in the problems are correct. (It's to prove that the pattern is always there that one needs induction.) If you just can't get these problems, don't worry about it. We don't expect everyone to be able to do them.
If you'd like an extra challenge, then try 7, 8, and 9.
Additional practice problems, with solutions, can be found here.
Section IIA (pp. 265-7): 1b,d; 2b,d; 3b,d; 4a,d
Exercise 3 asks you to schmatize 'no' statements in both the ways it is possible to do that. You need only do one way.
You should definitely do more of these for practice, but you only need to turn those ones in (though you can also turn in more if you want us to look at them).
Section IIB (pp. 267-71): 1a; 3a,c; 5b,c
Note: In 5b and 5c, the schemata are not equivalent, so you just need to produce an interpretation that makes one of them true and the other false. (In 5a and 5d, they are equivalent. See this handout for an example of how to do problems like that, though none of them are assigned, and we will develop a different method for showing equivalence (or implication, or validity) later.)
For an extra challenge, try some of the problems in IIC.
Additional practice problems, with solutions, can be found here.
Section IIIA (pp. 273-6): 1a,d,g; 2a,c; 3a,c; 5a,b; Extra Problem 3
For an extra challenge, try 8.
For problems 2a, 2c, 5a, 5b, and extra problem 3 (the 'unschematization' problems), do not worry too much about getting these into "idiomatic English". There are limits to how well one can really do that (especially without using English sentences that are ambiguous), and the point is not to render them in some form that your creative writing teacher would applaud. Rather, the point is for you to show that you understand what the schemata say.
You should definitely do more of these for practice, but you only need to turn the mentioned problems in (though you can also turn in more if you want us to look at them).
Additional practice problems, with solutions, can be found here.
Section IIIB (pp. 276-81): 1b,d; 2b,d,f; Extra Problem 4
Additional practice problems, with solutions, can be found here.
Section IIIB (pp. 276-81): 4a,b; 5; 6; 9; Extra Problem 5
Section IIIC (pp. 281-3): 1
Note: In 4a, the question is asking you to specify predicates of English that have the properties mentioned. For example, suppose we were asked for a predicate that is irreflexive, symmetric, and intransitive. Then "(1)+(2) is odd" would do. This is irreflexive [∀x¬(x+x is odd)], symmetric [∀x∀y(x+y is odd → y+x is odd)], and intransitive [∀x∀y∀z(x+y is odd ∧ y+z is odd → ¬(x+z is odd))]. The first two of these are obvious. For the last, if the antecedent holds, then either y is even, x and z are both odd, or y is odd, or x and z are both even. Either way, x+z is even.
Note: For problem (1), the idea is to show, e.g., that you can deduce ¬∀x(Fx) from ∃x(¬Fx) without using CQ, but only using the other rules of the system. Obviously, to show that CQ is dispensible in this sense, you would need to do all the cases. But, for this problem, you need only two cases; you can choose which ones to do.
For an extra challenge, try 15 or 16. If you are a 'math person', you might want to have a look at 14, as well. This is a version of what is known as Russell's Paradox. (Just replace "person" with "set" and "admires" with "contains (as a member)".) Another famous version concerns the barber who shaves only those Sevillians who do not shave themsevles. One can prove that this barber (if they exist) cannot live in Seville. I.e., one can prove, logically, that no one who lives in Seville shaves all and only those Sevillians who do not shave themselves.
Additional practice problems, with solutions, can be found here.