Mathematics

### Homework Assignments

#### Assigned Aug. 17

Sec. 1.1, problems 1a, b, c, g, h; 2e, g; 3a, c. To discuss Friday; don't turn in.

#### Assigned Aug. 19

Sec. 1.1, problems 3e, g; 7c, d; 9a, c; 11f, i, j, k. To discuss Monday; don't turn in.

#### Assigned Aug 22

Sec. 1.2, problems 8, 16f, 16g.
Also: Use truth tables to show that the propositional forms "P or Q" and "(not P) implies Q" are equivalent.
To discuss Wednesday; don't turn in.

#### Assigned Aug. 24

Sec. 1.2, problems 1 (all parts), 10d, g, j. To discuss Friday; don't turn in.

#### Assigned Aug. 26

Sec. 1.3, problems 1a, b, e, h, l, m, and 2 a, b, g, h. To discuss Monday; don't turn in.
Sec. 1.3, problems 1f, i, n, and 2i. Turn in Friday Sept. 2.

#### Assigned Aug. 29

Sec. 1.3, problems 1k, 2c, d, e, k, m, 9a, b, c, e, f. To discuss Wednesday; don't turn in.
Sec. 1.3, problems 2f, n. Turn in Friday Sept. 2.

#### Assigned Aug. 31

Sec. 1.4, problems 5c, f, i. Turn in Friday Sept. 9.

#### Assigned Sept. 2

Sec. 1.4, problems 11b, d, e. To discuss Wednesday; don't turn in.
Sec. 1.4, problems 6b, f, 7d, m. You should be able to do 6b with just two cases. Turn in Friday Sept. 9.

#### Assigned Sept. 9

Sec. 1.5, problems 12b, c, d. To discuss Monday; don't turn in.
Sec. 1.5, problems 3d, h, 4a, 5a, 6d. Turn in Friday Sept. 16.

#### Assigned Sept. 12

Prove: If a is a rational number other than 0, and b is an irrational number, then a/b is irrational. (real numbers) I suggest a proof by contradiction. Be sure your proof uses the assumption that a is not 0!
Sec. 1.6, problems 1b, 1g. In problem 1g you are trying to prove that there exists j such that m+2=4j-1.
Prove: If we are given five points in a square of side length 1, two of them are within a distance of sqrt(2)/2 of each other. Suggestion: Suppose no two of the points are within a distance of sqrt(2)/2 of each other. Divide the square into four smaller squares, all of equal size. How many points can be in each of the smaller squares?
Turn in Friday Sept. 16.

#### Assigned Sept. 15

Sec. 1.6, problems 1d, 2b (ignore complicated answer in text), d, 4d, e, 7d (you may assume that sqrt(3) is irrational). To discuss Monday; don't turn in.

#### Assigned Sept. 16

Sec. 1.6, problems 1h, 2e, 6j. To discuss Monday; don't turn in.

#### Assigned Sept. 26

Prove: For every b > 0 there exists an M > 0 such that if x > M then sqrt(x) > b. (Real numbers. You may assume: if 0 < x < y then 0 < sqrt(x) < sqrt(y).)
Sec. 2.1, problem 7. Suggestion: proof by contradiction.
Turn in Friday Sept. 30.

Sec. 2.1, problems 1abd, 4acij, 6a, 14a, 17ghijkl. To discuss Wednesday; don't turn in.

#### Assigned Sept. 28

Sec. 2.2, problems 7n, o, 8g, h, 9b, d, 10d, 12b. Turn in Wednesday, Oct. 5.
Sec. 2.2, problems 11b, f. To discuss Friday; don't turn in.

#### Assigned Oct. 7

Sec. 2.3, problems 1dkh, 5b, 6b.
Sec. 2.4, problems 6bd, 7ae, 8b. 6b: left hand side is sum from 1 to n of (8i-5).
Sec. 2.5, problems 2, 6b.
Turn in Friday Oct. 14.

#### Assigned Oct. 14

Sec. 2.2, problems 13a, 15c.
Sec. 3.2, problems 1gj, 5aeh.
Additional problem: Let R be the relation on Zx(Z-{0}) (Z=integers) given by: (a,b)R(c,d) if and only if ad=bc. Show that R is an equivalence relation. Find some members of the equivalence class of (2,3). What do all members of the equivalence class of (2,3) have in common?
Turn in Friday Oct. 28.

#### Assigned Oct. 21

Sec. 4.1, problems 2, 3bg (domain and range only), 7, 11af. Turn in Friday Oct. 28.

#### Assigned Oct. 26

Sec. 4.2, problem 1j.
Sec. 4.3, problems 1hl.
Turn in Friday Nov. 4.

#### Assigned Oct. 28, corrected Nov. 4

Sec. 4.3, problems 2ehl, 5, 9a, 11d (first show that it is a function). Turn in Friday Nov. 4.

#### Assigned Oct. 31

Sec. 4.3, problem 9a continued: show that the range is (0,infinity). Think of f as a function from R to (0,infinity), and find the inverse function.
Sec. 4.4, problem 1a (also find the inverse function).
Turn in Friday Nov. 4.

#### Assigned Nov. 11

Sec. 5.1, problems 1, 6b, 7, 12, 17.
Turn in by Tuesday Nov. 22.

#### Assigned Nov. 27

Sec. 5.2, problems 1, 3b d f.
Sec. 5.3, problems 3 (ignore the hint), 6 (just do n=3), 13a, 14b.
Don't turn in. To be discussed Friday Dec. 2.