Consider the set {1, 2, 3, 4, 5). (a) How many partitions of (1, 2, 3, 4, 5} have cardinality 1? (b) How many partitions of (1, 2, 3, 4, 5} have cardinality 2? (c) Which of the following are examples of partitions of (1, 2, 3, 4, 5) with cardinality 2? Yes No ? ? ? ? ? ? ? ? ? ? ? V V 5. {{4,5), (1,2,3}} V 1. {(2,3), (1,3,4,5}} 2. {(2,3)}, {5,1}} 3. {{5}, {1,2,3,4}} 4. {{2}, {1,3,4,5}} V 6. {{1,2}, {2,3), (3, d), (4,5}, {1,5}} 7. {{1,2), (3,4,5}} 8. {{2,5), (1,3,4}} 9. {{1,2}, {1,5}} 10. [0, {1, 2, 3, 4, 5}} 11. {{4}, {1,2,3,5}} 12. {{2,3}, {1,4,5}} 13. {{1,4), (2, 3, 5}}
Consider the set {1, 2, 3, 4, 5). (a) How many partitions of (1, 2, 3, 4, 5} have cardinality 1? (b) How many partitions of (1, 2, 3, 4, 5} have cardinality 2? (c) Which of the following are examples of partitions of (1, 2, 3, 4, 5) with cardinality 2? Yes No ? ? ? ? ? ? ? ? ? ? ? V V 5. {{4,5), (1,2,3}} V 1. {(2,3), (1,3,4,5}} 2. {(2,3)}, {5,1}} 3. {{5}, {1,2,3,4}} 4. {{2}, {1,3,4,5}} V 6. {{1,2}, {2,3), (3, d), (4,5}, {1,5}} 7. {{1,2), (3,4,5}} 8. {{2,5), (1,3,4}} 9. {{1,2}, {1,5}} 10. [0, {1, 2, 3, 4, 5}} 11. {{4}, {1,2,3,5}} 12. {{2,3}, {1,4,5}} 13. {{1,4), (2, 3, 5}}
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the set (1, 2, 3, 4, 5).
(a) How many partitions of (1, 2, 3, 4, 5} have cardinality 1?
(b) How many partitions of (1, 2, 3, 4, 5} have cardinality 2?
(c) Which of the following are examples of partitions of (1, 2, 3, 4, 5) with cardinality 2?
Yes 1. {{2,3}, {1,3,4,5}}
2. {(2,3), (5,1}}
3. {{5}, {1,2,3,4}}
4. {{2}, {1,3,4,5}}
5. {{4,5}, {1,2,3}}
6. {(1,2), (2,3), (3, d), (4,5}, {1,5}}
7. {{1,2}, {3,4,5)}}
8. {(2,5), (1,3,4}}
9. {{1,2}, {1,5}}
10. {0, 1, 2, 3, 4, 5}}
11. {{4}, {1,2,3,5}}
12. {{2,3), (1,4,5}}
13. [[1,4), (2,3,5}}
No
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