MAT 108: Introduction to Abstract Mathematics (Fall 2013)

MAT 108: Introduction to Abstract Mathematics (Fall 2013)

Homework Assignments

Each assignment is due by the end of lecture on the given date. Late homework will not be accepted. Solve the assigned problems in order, staple the properly assembled pages, and print your name clearly on the front page and write the number of your section (either A1, A2, or A3) in red on the top right corner of the front page. Do not fold. Your assignment will be graded and then then returned to you in the discussion session. Assignments will be graded not only on correctness but also on the quality of writing; in particular, the reader is instructed to stop reading if a solution is incoherent.

In each section of the book, some problems are labeled by the star (*), which means that their answers are given in the back. For practice, do as many of these as you judge necessary. The problems listed below are those that you need to turn in (unless explicitly stated otherwise). If you are using an earlier edition of the book please make sure that you are working on the right problems.

Some solutions will be provided, but will not be carefully proofread, so check for mistakes!

Due Date Problems
Fri., Oct. 4 Read the writing tips and do the informal exercise suggested at the end.

The Liar and Truthteller puzzle is one of the most famous mathematical puzzles. It is described in the second problem of this selection of logical puzzles. Most of these problems are very hard, much beyond what you will be expected to do. Try to do the first two on your own, then read the solutions. If you really want to be seriously confused, think about the third problem.

Do not turn anything in on this assignment.

HW1 Fri., Oct. 11 1.1: 3(h), 4(d), 6(h), 9(a), 10(b).

1.2: 3(e), 5(d), 6(b), 7(a), 12(f), 16(b).

1.3: 6(c), 8(c), 10(c), 10(e).

1.4: 4(b), 5(f), 6(f), 8(a), 9(d), 11(b).

Extra problems for you to think about. Do not turn anything in on these two extra problems.

Solutions.

HW2 Fri., Oct. 18 1.5: 3(g), 4(c), 5(c), 6(e), 7(b). 10, 12(d).

1.6: 4(b), 4(c), 4(g), 5(a), 6(i), 7(h).

Especially if you are a computer science student, you need to know about Satisfiability. The satisfiability part of the homework is optional; do not turn anything in.

Solutions.

HW3 Fri., Oct. 25 2.1: 5(d), 5(j), 6(d), 14(d), 15(c), 15(h), 17(d), 19(g).

2.2: 1(j), 2(f), 9(b), 9(c), 11(b), 12(b), 12(c), 19(f).

2.3: 1(n).

2.4: 6(g), 7(a), 7(h), 8(h), 13(c).

Think on your own about problems 4 and 5 from the selection of logical puzzles, and relate them to mathematical induction. Then read the solutions. Problem 7 is another (very difficult) problem of similar type. Do not turn anything in on these puzzles.

Solutions.

HW4 Fri., Nov. 1 2.5: 1(b), 2, 5(b), 5(c), 13(c).

3.1: 1, 2(b), 4(d), 5(a), 5(h), 7(c), 7(d), 7(f), 15(c).

Solutions.

HW5 Fri., Nov. 8 3.2: 1(b), 1(c), 1(f), 5(b), 5(e), 5(f), 5(h), 7(b), 7(d), 9(a), 11, 12, 13(c), 19(d).

3.3: 2(a), 2(c), 3(a), 3(d), 4, 7(b), 7(c), 15(c).

4.1: 1(b), 1(c), 1(i) (In problem 1, one codomain suffices), 4(d), 6(d), 11(e), 19(e).

Solutions.

HW6 Fri., Nov. 15 4.2: 1(b), 10, 13, 14(c), 14(d).

4.3: 1(b), 1(d), 1(f), 1(h), 1(l), 2(b), 2(d), 2(f), 2(h), 2(l), 3(c), 6, 8(c), 8(d), 14(c).

Solutions.

HW7 Fri., Nov. 22 4.4: 1(a), 2(b), 2(c) (find a simpler function than 3(d)!), 3(a), 3(d), 5(b).

4.5: 1(b), 2(b), 2(e), 5(a), 5(b), 10(a), 10(b), 13, 18(a), 18(b). Also, find a counterexample to equality in 10(a).

Solutions.

HW8 Fri., Dec. 6 No homework for Thanksgiving week, and no discussion on Tue., Nov. 26.

5.1: 2(k), 2(l), 2(m), 2(o), 4, 6(b), 11(d), 12, 21(b), 22(a).

Typo corrected: previous version listed 1(k), 1(l), 1(m), 1(o) that do not exist.

5.2: 3(c), 4(c), 7(b), 7(d), 7(g), 12(b).

5.3: 2, 9(c), 9(e), 9(f), 10(a), 10(b), 10(d), 13(a), 14(a), 14(b).

5.4: 2, 5(a), 5(e), 8(a), 8(b).

Solutions.