For exam practice, solve the following problems from the book. These are selected so that the amount of work is a bit larger than the amount of work on the actual exam, so I recommend working under a time limit of about 60 minutes. Solutions will not be provided.
1.1: 4(c), 4(f)
1.2: 7(c), 16(d)
1.3: 8(h), 10(a), 10(d), 10(f) (with proofs)
1.5: 4(b)
1.6: 4(h), 4(i)
2.2: 10(c), 11(e)
2.4: 6(i), 7(e), 7(i), 8(a)
Solutions to Midterm 1.

For exam practice, solve the following problems from the book. These are selected so that the amount of work is a bit larger than the amount of work on the actual exam, so I recommend working under a time limit of about 60 minutes. Solutions will not be provided.
3.1: 5(b)(d) (Assume both are relations on {1,2,3,4,5}. Give the domains and ranges of all relations, and make sure you can determine at a glance reflexivity, symmetry, transitivity, or lack thereof.), 8(d)
3.2: 5(e) (describe all equivalence classes), 7(a), 7(c), 13(b), 15(a)
3.3: 5 (also prove that it is an equivalence relation)
4.1: 5(b) (Is this function one-to-one? What is its range?), 6(b)
4.2: 5(c) (Let A be the natural domain of f, and B be the range of f. Determine A and B. Assume f:A-> B. Then answer the question.), 20 (Give your own proof without looking at the correct proof in the book. Give a counterexample when f is not assumed to have an inverse.)
4.3: 3(d), 7(b), 8(a)
4.4: 4
4.5: 10(c)
Solutions to Midterm 2.