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.) 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 are also encouraged to work on the problems together—though, of course, submitted material should be a student's own work.
Students often request a source of additional problems to use for practice. One option is to find almost any other logic textbook than the one we use: It'll be sure to have problems. A second is to download this old set of logic problems that I used when I taught logic at Harvard back in 2002. Some of these problems will overlap with ones in the book; many will not, however. You can also download solutions to some of the problems.
Section IA (pp. 253-5): 1b,e; 2, 3; 4b,d,g,k
Section IB (pp. 255-60): 1a; 2a,c; 3a,c; 4a,d; 6; 7b; Section IC (pp. 260-4): 2; 3a,c; 5; 7; 11b,d; Extra Problems 1-2
Section IIA (pp. 265-7): 1b; 2b; 3b; 4a,f; Section IIB (pp. 267-71): 1a,c; 3a,b,e,f; 5a,c
Section IIIA (pp. 273-6): 1a,c,e; 2a,c; 3a,b,c; 5a,b; Extra Problem 3
Section IIIB (pp. 276-81): 1b,d; 2a,c,e; Extra Problem 4
Section IIIB (pp. 276-81): 4a,b,c; 7; 11; 14; 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 first two hold, then either x and z are both odd, and y is even, or x and z are both even, and y is odd. Either way, x+z is even.
Section IV (pp. 284-8): 1b; 2a; 3a; 5a,c; 6
Section IIIC (pp. 281-3): 1; 3; 5; 6; 7