$$\bar{A} \cap \bar{B}$$

A > B

$$\bar{A} \cup \bar{B}$$      $\overline{A \cap B}$

A ø B

$$20 \begin{bmatrix} 1 \ 0 \ 1 \end{bmatrix}, \begin{bmatrix} 0 \ 1 \ 0 \end{bmatrix}, \begin{bmatrix} -1 \ 0 \ 1 \end{bmatrix}$$

21 After 100 迭代次数向下取整为最接近的整数 70 98 136 56 78 109 以及最大特征值为 42 59 81 0.9963, 0.9996, 1.0029 21 29 40

22 (a) 3, 1; $$\begin{bmatrix} 0.7071 \ 0.7071 \end{bmatrix}, \begin{bmatrix} 0.7071 \ -0.7071 \end{bmatrix}$$

(b) 0.8794, −1.3473, −2.5321;

26 $$E_1 = 4E_2 + 3I_2; I_1 = 3E_2 + \frac{5}{2}I_2$$

CHAPTER 6

Exercises

1 A = {1, 2, 3, 4, 5, 6, 7, 8, 9}

$$B = {-4, 4}$$

$$C = {5, 6, 7, 8, 9, 10}$$

$$D = {4, 8, 12, 16, 20, 24}$$

2 A < B = {−4, 1, 2, 3, 4, 5, 6, 7, 8, 9}

$$A \cap B = {4}$$

$$A \cup C = {n \in \mathbb{N}: 1 \leq n \leq 10}$$

$$A \cap C = {n \in \mathbb{N}: 5 \leq n \leq 9}$$

B < D = {−4, 4, 8, 12, 16, 20, 24}

$$B \cap D = {4}$$

$$B \cap C = \emptyset$$

3 $$A \cup B = {n \in \mathbb{N}: 1 \leq n \leq 10}$$

$$A \cap C = {1, 5, 9}$$

$$A \cap B = \emptyset$$

$$B \cup C = {1, 2, 4, 5, 6, 8, 9, 10}$$

$$B \cap C = {4, 8}$$

4

5 (a) $$A \cup B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20}$$

(b) $$A \cap B = {2, 4, 6, 8, 10}$$

(c) $$A \cup C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 16, 32}$$

(d) $$A \cap C = {2, 4, 8}$$

6 (a) True

(b) False

(c) False

7 (a) $${n \in \mathbb{N}: 11 \leq n \leq 32}$$

(b) {11, 13, 15, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}

(c) $$\bar{A} = {n \in \mathbb{N}: 11 \leq n \leq 32}$$

$$\bar{B} = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}$$

(d) $$\overline{A \cap B} = {1, 3, 5, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}$$

(e) $$\bar{A} \cup \bar{B} = \bar{A} \cap \bar{B}$$ (see (d))

11 (a) $$A \cap B$$ (b) $\emptyset$ (c) $A$

(d) $$U$$

(d) $$U$$ (e) $A$ (f) $A \cup (B \cap C)$
(g) $A \cap (B \cap C)$

(g) $$A + 1 + (D + 1) + C$$ )

14 (a) 5 (b) 25

15 (a) 20 (b) 27

16 4

17 (a) $$\bar{C} = {a, b, d, i}$$ , $\overline{B \cup C} = {a, b, i}$

$$\bar{B} \cap \bar{C} = {a, b, i}$$ , $A \cap B \cap D = \emptyset$
$A \cup F = {a, b, c, f, i}$ , $D \cup (E \cap F) = {b, c, e, h, i}$ ,
$(D \cup E) \cap F = {b, c, i}$

(b) $$B \cup C = {c, d, e, f, g, h}$$ , $C \cup E = {c, e, f, g, h, i}$
$D \cup E \cup F = {b, c, e, f, h, i}$

(c) $$L_1: {b, c, d, e, f, g, h, i}$$

L2: {b, c, d, e, f, g, h, i}

L3: 所有元素

18 (a) 1 if $$p = 1, q = 1$$ ; 0 otherwise

(b) 0 if $$p = 0, q = 0$$ ; 1 otherwise

(c) 0 (d) 1

19 (a) $$p \cdot q + \bar{p} \cdot \bar{q}$$

(b) $$(p + \bar{p}) \cdot (q + \bar{q})$$

(c) $$p + q + \bar{p} + \bar{q}$$

(d) $$p \cdot q + r \cdot s$$

(e) $$\bar{p} \cdot q \cdot s + \bar{p} \cdot \bar{q} \cdot r \cdot s + p \cdot q \cdot r \cdot s + p \cdot \bar{q} \cdot s + p \cdot q \cdot s$$

(f) $$p \cdot q \cdot r + p \cdot q \cdot t + p \cdot q \cdot u + p \cdot s \cdot \bar{u} + p \cdot v$$

20 $$\bar{p} \cdot \bar{q} + r + \bar{s} + \bar{q} \cdot t$$