80 lines
7.7 KiB
Markdown
80 lines
7.7 KiB
Markdown
#public
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# Homework
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Questions (P7.)
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1. a
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1. A. True
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2. B. Order does not matter in sets
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2. MISSISSIPPI
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3.
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1. $\subseteq$
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2. $\in$
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3. $\subseteq$
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4. $\in$
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5. $\in$ x wrong $\emptyset$ is a $\subseteq$ of all sets
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6. $\subseteq$
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4. 9.
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1. a) $\{S_4, S_5, S_9\}$
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2. b) **??**
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3. c) quadrillion
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4. d)
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1. F
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2. T (if order does not matter)
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3. T
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4. F
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5. T
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6. T
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7. F
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8. F
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9. F
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10. T
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11. F
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12. F
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13. T
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14. F
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15. T
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16. T
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5. 10.
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1. $D_1=\{1\}, D_2=\{1,2\}, D_{10}=\{1,2,5\}$
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2. b)
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1. T
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2. F
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3. T
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4. T
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5. T?
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6. F
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7. T
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8. F
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9. F
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10. F
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11. F
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12. T
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3. c) $|D_{10}|=3$, $|D_{19}|=2$
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4. D) $|\mathcal{D}|=9$
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| Questions | Answer |
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| --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------- |
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| 1. <br> 1. (a) True or false? {red, white, blue} = {white, blue, red}. <br> 2. (b) What is wrong with this statement: Red is the first element of the set {red, white, blue}? | a. True<br>b. Order does not matter in sets |
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| 2. Which has the larger cardinality? The set of letters in the word MISSISSIPPI or the set of letters in the word FLORIDA ? | MISSIPPI |
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| 3. Fill in the blank with the appropriate symbol, ∈ or ⊆. <br> 1. (a) {1, 2, 3} {1, 2, 3, 4} <br> 2. (b) 3 {1, 2, 3, 4} <br> 3. (c) {3} {1, 2, 3, 4} <br> 4. (d) {𝑎} {{𝑎}, {𝑏}, {𝑎, 𝑏}} <br> 5. (e) ∅ {{𝑎}, {𝑏}, {𝑎, 𝑏}} <br> 6. (f) {{𝑎}, {𝑏}} {{𝑎}, {𝑏}, {𝑎, 𝑏}} | |
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| 9. Let 𝑆1 = {𝑜, 𝑛, 𝑒}, 𝑆2 = {𝑡, 𝑤, 𝑜}, 𝑆3 = {𝑡, ℎ, 𝑟, 𝑒, 𝑒}, and so on. <br> 1. (a) Find all 𝑘 ∈ {1, 2, . . . , 10} with \|𝑆𝑘\| = 4. <br> 2. (b) Find distinct indices 𝑗, 𝑘 ∈ ℕ with 𝑆𝑗 = 𝑆𝑘. <br> 3. (c) Find the smallest value of 𝑘 ∈ ℕ with 𝑎 ∈ 𝑆𝑘. <br> 4. (d) Let 𝒮 = {𝑆𝑘}40 𝑘=1. Determine whether the following statements are true or false. <br> 1. (i) 𝑆13 = {𝑛, 𝑒, 𝑖, 𝑡, ℎ, 𝑒, 𝑟} <br> 2. (ii) {𝑛, 𝑒, 𝑡} ⊆ 𝑆20 <br> 3. (iii) 𝑆1 ∈ 𝒮 <br> 4. (iv) 𝑆3 ⊆ 𝒮 <br> 5. (v) ∅ ∈ 𝒮 <br> 6. (vi) ∅ ⊂ 𝒮 <br> 7. (vii) ∅ ⊆ 𝒮 <br> 8. (viii) 𝑆1 ⊆ 𝑆11 <br> 9. (ix) 𝑆1 ⊆ 𝑆21 <br> 10. (x) 𝑆1 ⊂ 𝑆21<br> 11. (xi) {𝑛, 𝑖, 𝑒} ∈ 𝒮 <br> 12. (xii) {{𝑓, 𝑜, 𝑢, 𝑟}} ⊆ 𝒮 <br> 13. (xiii) 𝑢 ∈ 𝑆40 <br> 14. (xiv) 𝒫(𝑆9) ⊆ 𝒫(𝑆19) <br> 15. (xv) {𝑠, 𝑖} ∈ 𝒫(𝑆6) <br> 16. (xvi) 𝑤 ∈ 𝒫(𝑆2) | |
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| 10. For 𝑘 ∈ {1, 2, . . . , 20}, let 𝐷𝑘 = {𝑥 ∣ 𝑥 is a prime number which divides 𝑘} and let 𝒟 = {𝐷𝑘 ∣ 𝑘 ∈ {1, 2, . . . , 20}}.<br> 1. (a) Find 𝐷1, 𝐷2, 𝐷10, and 𝐷20. <br> 2. (b) True or False: <br> 1. (i) 𝐷2 ⊂ 𝐷10 <br> 2. (ii) 𝐷7 ⊆ 𝐷10 <br> 3. (iii) 𝐷10 ⊂ 𝐷20 <br> 4. (iv) ∅ ∈ 𝒟 <br> 5. (v) ∅ ⊂ 𝒟 <br> 6. (vi) 5 ∈ 𝒟 <br> 7. (vii) {5} ∈ 𝒟 <br> 8. (viii) {4, 5} ∈ 𝒟 <br> 9. (ix) {{3}} ⊆ 𝒟 <br> 10. (x) 𝒫(𝐷9) ⊆ 𝒫(𝐷6) <br> 11. (xi) 𝒫({3, 4}) ⊆ 𝒟 <br> 12. (xii) {2, 3} ∈ 𝒫(𝐷12) <br> 3. (c) Find \|𝐷10\| and \|𝐷19\|. <br> 4. (d) Find \|𝒟\| | |
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# Unit 1
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## Krish Hw 2
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1. A = {1, 2, 3}, B = {2, 3, 4} and C = {1, 2, 4}. List the elements of the specified set
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1. (a) A ∩ B; | {2,3}
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2. (b) A ∪ B; | {1,2,3,4}
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3. (c) C\A; | {1}
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4. (d) A ∪ (B ∩ C); | {2,1,3}
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5. (e) (A ∩ C) ∪ (B ∩ C); | {1,2,4}
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6. (f) A × B; | {(1,2),(1,3),(1,4),(2,3),(2,2),(2,4),(3,2),(3,3),(3,4)}
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7. (g) B × A; | {(2,1),(2,2),(2,3),(3,1),(3,2),(3,3),(4,1),(4,2) ,(4,3)}
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8. (h) (A × B) ∩ (B × A). | {(2,2),(3,3)}
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2. $M_2$ = {2, 4, 6, 8, 10, · · · } and $M_3$ = {3, 6, 9, 12, 15, · · · }. Find:
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1. (a) $M_2$ ∩ $M_3$;
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1. $M_6$
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2. (b) $M_3 \backslash M_2$
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1. $\{x|x=6k-3 \space\forall\space k \in\mathbb{N}\}$
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