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.
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. Note that what you're being asked to show, in Problem 6, for example, is that every schema constructed using just sentence-letters, conjunction, and disjunction is satisfiable but not valid, including ones that contain (say) 100 sentence-letters and who knows how many ands and ors. There are infinitely many such schemata, so it is not possible to check them all.
Real proofs would use mathematical induction, and we do not expect anyone to give such a proof. 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, or 9.
Additional practice problems, with solutions, can be found here.
Section IIA (pp. 265-7): 1b,d; 2b,d; 3b,d (you need only do these once, as a negated existential); 4a,d
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
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
NOTE: See this file for re-written versions of some of the formulas on the problem set.
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. For an extra challenge, try 8.
Additional practice problems, with solutions, can be found here.
Section IIIB (pp. 276-81): 1b,d; 2b,d,f; Extra Problem 4
NOTE: See this file for re-written versions of some of the formulas on the problem set.
Additional practice problems, with solutions, can be found here.
Section IIIB (pp. 276-81): 4a,b; 5; 6; 9; Extra Problem 5
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 (i) y is even and x and z are both odd or (ii) y is odd and x and z are both even. Either way, x+z is even.
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)".)
Additional practice problems, with solutions, can be found here.
Section IV (pp. 284-8): 2b; 3b; 4b,d
Optional: Section IIIC (pp. 281-3): 1; 3
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 one case; you can choose which one to do.