#public
# Homework
Questions (P7.)
1. a
1. A. True
2. B. Order does not matter in sets
2. MISSISSIPPI
3.
1. $\subseteq$
2. $\in$
3. $\subseteq$
4. $\in$
5. $\in$ x wrong $\emptyset$ is a $\subseteq$ of all sets
6. $\subseteq$
4. 9.
1. a) $\{S_4, S_5, S_9\}$
2. b) **??**
3. c) quadrillion
4. d)
1. F
2. T (if order does not matter)
3. T
4. F
5. T
6. T
7. F
8. F
9. F
10. T
11. F
12. F
13. T
14. F
15. T
16. T
5. 10.
1. $D_1=\{1\}, D_2=\{1,2\}, D_{10}=\{1,2,5\}$
2. b)
1. T
2. F
3. T
4. T
5. T?
6. F
7. T
8. F
9. F
10. F
11. F
12. T
3. c) $|D_{10}|=3$, $|D_{19}|=2$
4. D) $|\mathcal{D}|=9$
| Questions | Answer |
| --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------- |
| 1.
1. (a) True or false? {red, white, blue} = {white, blue, red}.
2. (b) What is wrong with this statement: Red is the first element of the set {red, white, blue}? | a. True
b. Order does not matter in sets |
| 2. Which has the larger cardinality? The set of letters in the word MISSISSIPPI or the set of letters in the word FLORIDA ? | MISSIPPI |
| 3. Fill in the blank with the appropriate symbol, โ or โ.
1. (a) {1, 2, 3} {1, 2, 3, 4}
2. (b) 3 {1, 2, 3, 4}
3. (c) {3} {1, 2, 3, 4}
4. (d) {๐} {{๐}, {๐}, {๐, ๐}}
5. (e) โ
{{๐}, {๐}, {๐, ๐}}
6. (f) {{๐}, {๐}} {{๐}, {๐}, {๐, ๐}} | |
| 9. Let ๐1 = {๐, ๐, ๐}, ๐2 = {๐ก, ๐ค, ๐}, ๐3 = {๐ก, โ, ๐, ๐, ๐}, and so on.
1. (a) Find all ๐ โ {1, 2, . . . , 10} with \|๐๐\| = 4.
2. (b) Find distinct indices ๐, ๐ โ โ with ๐๐ = ๐๐.
3. (c) Find the smallest value of ๐ โ โ with ๐ โ ๐๐.
4. (d) Let ๐ฎ = {๐๐}40 ๐=1. Determine whether the following statements are true or false.
1. (i) ๐13 = {๐, ๐, ๐, ๐ก, โ, ๐, ๐}
2. (ii) {๐, ๐, ๐ก} โ ๐20
3. (iii) ๐1 โ ๐ฎ
4. (iv) ๐3 โ ๐ฎ
5. (v) โ
โ ๐ฎ
6. (vi) โ
โ ๐ฎ
7. (vii) โ
โ ๐ฎ
8. (viii) ๐1 โ ๐11
9. (ix) ๐1 โ ๐21
10. (x) ๐1 โ ๐21
11. (xi) {๐, ๐, ๐} โ ๐ฎ
12. (xii) {{๐, ๐, ๐ข, ๐}} โ ๐ฎ
13. (xiii) ๐ข โ ๐40
14. (xiv) ๐ซ(๐9) โ ๐ซ(๐19)
15. (xv) {๐ , ๐} โ ๐ซ(๐6)
16. (xvi) ๐ค โ ๐ซ(๐2) | |
| 10. For ๐ โ {1, 2, . . . , 20}, let ๐ท๐ = {๐ฅ โฃ ๐ฅ is a prime number which divides ๐} and let ๐ = {๐ท๐ โฃ ๐ โ {1, 2, . . . , 20}}.
1. (a) Find ๐ท1, ๐ท2, ๐ท10, and ๐ท20.
2. (b) True or False:
1. (i) ๐ท2 โ ๐ท10
2. (ii) ๐ท7 โ ๐ท10
3. (iii) ๐ท10 โ ๐ท20
4. (iv) โ
โ ๐
5. (v) โ
โ ๐
6. (vi) 5 โ ๐
7. (vii) {5} โ ๐
8. (viii) {4, 5} โ ๐
9. (ix) {{3}} โ ๐
10. (x) ๐ซ(๐ท9) โ ๐ซ(๐ท6)
11. (xi) ๐ซ({3, 4}) โ ๐
12. (xii) {2, 3} โ ๐ซ(๐ท12)
3. (c) Find \|๐ท10\| and \|๐ท19\|.
4. (d) Find \|๐\| | |
# Unit 1
## Krish Hw 2
1. A = {1, 2, 3}, B = {2, 3, 4} and C = {1, 2, 4}. List the elements of the specified set
1. (a) A โฉ B; | {2,3}
2. (b) A โช B; | {1,2,3,4}
3. (c) C\A; | {1}
4. (d) A โช (B โฉ C); | {2,1,3}
5. (e) (A โฉ C) โช (B โฉ C); | {1,2,4}
6. (f) A ร B; | {(1,2),(1,3),(1,4),(2,3),(2,2),(2,4),(3,2),(3,3),(3,4)}
7. (g) B ร A; | {(2,1),(2,2),(2,3),(3,1),(3,2),(3,3),(4,1),(4,2) ,(4,3)}
8. (h) (A ร B) โฉ (B ร A). | {(2,2),(3,3)}
2. $M_2$ = {2, 4, 6, 8, 10, ยท ยท ยท } and $M_3$ = {3, 6, 9, 12, 15, ยท ยท ยท }. Find:
1. (a) $M_2$ โฉ $M_3$;
1. $M_6$
2. (b) $M_3 \backslash M_2$
1. $\{x|x=6k-3 \space\forall\space k \in\mathbb{N}\}$