- •Множества и отношения
- •Содержание
- •1. Цель расчетно-графического задания
- •2. Общие положения и требования к отчету
- •3. Основные теоретические сведения
- •3.1. Элементы теории множеств
- •Инволютивность:
- •Законы де Моргана:
- •Выражение для разности:
- •3.2. Отношения
- •4. Варианты индивидуальных заданий
- •5. Порядок выполнения ргз
- •6. Контрольные вопросы
- •Библиографический список
- •Приложение а. Пример оформления титульного листа.
- •Приложение б. Пример решения задачи о минимальном покрытии.
4. Варианты индивидуальных заданий
З адание 1. Заданы множества A, B, C. Построить X=A B, Y=A B, Z=A\B и C, если U ={ ui | ui N & ui ≤ 20 }. Для полученных Y и Z найти Y×Z .
1. A={ 2,3,4,5,6,16 } 2. A={ 2,3,14,5,8,18 }
B={ 5,6,20,15,11,1,16 } B={ 5,18,20,15,11,1,2 }
C={ 11,3,5,14,7,8,6,17 } C={ 1,13,5,14,7,8,6,19 }
3. A={ 12,3,14,9,6,18 } 4. A={ 2,13,14,7,6,18 }
B={ 5,6,3,15,11,1,16 } B={ 6,2,15,13,18,3 }
C={ 19,3,9,14,7,8,6,11 } C={ 20,3,9,4,7,8,6,17 }
5. A={ 2,3,4,8,6,15 } 6. A={ 2,3,9,8,16,20 }
B={ 5,6,20,1 0,11,1,15 } B={ 5,6,2,20,11,1,16 }
C={ 11,3,5,4,7,8,9,10 } C={ 11,3,15,4,17,5,9,1 }
7. A={ 2,3,4,5,11,16 } 8. A={ 4,3,14,5,10,6 }
B={ 5,6,1,11,9,16 } B={ 5,6,1,10,9,3 }
C={ 10,3,15,4,7,8,6,18 } C={ 10,13,5,4,7,2,6,18 }
9. A={ 12,6,14,1,8,16 } 10. A={ 12,6,11,7,10,19 }
B={ 5,6,1,11,9,20 } B={ 15,6,8,11,19,20 }
C={ 2,3,11,4,7,18,6,10 } C={ 5,9,10,4,7,8,6,20 }
11. A={ 16,6,10,1,2,8 } 12. A={ 16,6,10,1,2,8 }
B={ 5,6,1,11,9,10 } B={ 5,6,1,11,9,10 }
C={ 2,3,11,4,8,17,6,12 } C={ 11,4,8,2,3,17,6,12 }
13. A={ 5,6,14,1,8,16 } 14. A={ 15,8,14,10,9,6 }
B={ 6,1, 5,11,9,2 } B={ 6,1,8,11,9,2,20 }
C={ 12,3,1,4,17,8,6,10 } C={ 8,16,12,13,7,4,9, 10 }
15. A={ 20,19,14,3,8,11 } 16. A={ 12,1,14,13,8,2 }
B={ 5,6,3,11,9,20 } B={ 2,6,3,1,9,20 }
C={ 2,3,11,14,7, 8,16,10 } C={ 13,11,4,7,18,2,16,10 }
17. A={ 12,3,14,11,5,1,13 } 18. A={ 10,14,12,8,15,1,13 }
B={ 5,6,1,13,9,18 } B={ 5,6,1,13,9,8 }
C={ 12,3,10,4,7,18,6,1 } C={ 12,9,10,4,17,5,6,1 }
19. A={ 4,6,14,7,8,19 } 20. A={ 12,7,14,6,8,9 }
B={ 6,1,11,4,9,20 } B={ 6,14,11,4,9,20 }
C={ 2,3,10,4,11,18,6,13 } C={ 12,15,1,4,20,18,6,13 }
21. A={ 7,16,14,2,8,19 } 22. A={ 12,15,4,6,10,9 }
B={ 2,1,11,4,19,20 } B={ 6,14,11,4,9,20 }
C={ 12,20,4,11,18,6,3,13 } C={ 20,15,1,4,3,18,6,13 }
21. A={ 14,6,17,3,18,2 } 24. A={ 15,7,14,6,18,19 }
B={ 6,1,11,14,9,12 } B={ 6,14,11,14,19,20 }
C={ 2,3,20,14,1,18,6,13 } C={ 2,15,1,4,20,8,16,3 }
25. A={ 14,5,14,17,8,9 }
B={ 6,1,11,14,9,18 }
C={ 2,15,16,11,4,20,8,13 }
Задание 2. Построить множество всех подмножеств множества Y, полученного при выполнении задания 1.
Задание 3. Упростить выражение.
1 . C B D B D A D C B D
2. A B C A B A C A C B
3. A B A C A C A B C B C
4. A B C A B C A C A B
5. C B B C A B C A D A B D
6. A B C D A C B A B D
7. A B D A B C A B B C
8. A B C A B C A B C C
9. A ((B C) (B D) B D) A D A C
10. (A B D) C A C (C A) B
11. A B C A B C D A B C
12. A (A B C (A B C) A C) A C A D
1 3. C B D B D A D C B D
14. A B C A B A C A C B C
15. A B A C A C A B C B C
16. A B C A B C A C A B
17. B C B C D B C A A B D
18. B A D C A C B A B D
19. A B D A B C A B D C
20. B A C A B C A B C C
2 1. C B D B D A D C B D
22. C B D D B A D C B D
23. A B C A B A C A C B
24. A B A C A C A B C B C
25. A B C A B C A C A B
Задание 4. Заданы отношения R1.и R2 . Построить R1 R2 , R1 R2 , R1 и R1 º R2 .
1 . 2.
R1 |
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3. 4.
R1 |
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5. 6.
R1 |
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R1 |
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7. 8.
R1 |
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R1 |
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9. 10.
R1 |
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R1 |
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11. 12.
R1 |
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R1 |
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13. 14.
R1 |
y1 |
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R1 |
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15. 16.
R1 |
y1 |
y2 |
y3 |
y4 |
x1 |
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y3 |
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y4 |
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R1 |
y1 |
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y3 |
y4 |
x1 |
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17. 18.
R1 |
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y3 |
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x1 |
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z3 |
y1 |
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y3 |
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y4 |
1 |
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R1 |
y1 |
y2 |
y3 |
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x1 |
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R2 |
z1 |
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19. 20.
R1 |
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x1 |
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R1 |
y1 |
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21. 22.
R1 |
y1 |
y2 |
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y4 |
x1 |
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R1 |
y1 |
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y3 |
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x1 |
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х2 |
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y1 |
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23. 24.
R1 |
y1 |
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y3 |
y4 |
x1 |
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y4 |
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R1 |
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x1 |
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R2 |
z1 |
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y1 |
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25.
R1 |
y1 |
y2 |
y3 |
y4 |
x1 |
1 |
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х2 |
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х3 |
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y4 |
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Задание 5. На множестве Х задано отношение несовместимости R. Построить все максимальные совместимые подмножества множества Х.
1 2 3
R |
x1 |
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x5 |
x6 |
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R |
x1 |
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x4 |
x5 |
x6 |
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R |
x1 |
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x3 |
x4 |
x5 |
x6 |
x1 |
– |
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4 5 6
R |
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R |
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R |
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x3 |
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7 8 9
R |
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R |
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R |
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x6 |
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x1 |
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x3 |
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x4 |
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1 |
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x4 |
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x4 |
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|
x5 |
1 |
1 |
|
1 |
– |
|
|
x5 |
1 |
|
|
1 |
– |
|
|
x5 |
1 |
|
1 |
|
– |
1 |
x6 |
1 |
|
1 |
1 |
|
– |
|
x6 |
1 |
|
1 |
1 |
|
– |
|
x6 |
1 |
1 |
|
|
1 |
– |
10 11 12
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
|
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
|
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
x1 |
– |
1 |
|
|
|
1 |
|
x1 |
– |
|
1 |
1 |
|
1 |
|
x1 |
– |
1 |
|
1 |
|
1 |
x2 |
1 |
– |
|
1 |
1 |
|
|
x2 |
|
– |
1 |
|
1 |
|
|
x2 |
1 |
– |
|
|
1 |
1 |
x3 |
|
|
– |
1 |
1 |
1 |
|
x3 |
1 |
1 |
– |
|
|
1 |
|
x3 |
|
|
– |
1 |
1 |
|
x4 |
|
1 |
1 |
– |
|
1 |
|
x4 |
1 |
|
|
– |
1 |
|
|
x4 |
1 |
|
1 |
– |
|
|
x5 |
1 |
1 |
|
|
– |
|
|
x5 |
|
1 |
|
1 |
– |
1 |
|
x5 |
|
1 |
1 |
|
– |
1 |
x6 |
1 |
|
1 |
1 |
|
– |
|
x6 |
1 |
|
1 |
|
1 |
– |
|
x6 |
1 |
1 |
|
|
1 |
– |
13 14 15
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
|
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
|
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
x1 |
– |
1 |
|
1 |
|
1 |
|
x1 |
– |
|
1 |
|
1 |
1 |
|
x1 |
– |
|
|
1 |
1 |
|
x2 |
1 |
– |
1 |
|
|
1 |
|
x2 |
|
– |
1 |
1 |
1 |
|
|
x2 |
|
– |
1 |
1 |
|
|
x3 |
|
1 |
– |
1 |
1 |
|
|
x3 |
1 |
1 |
– |
|
|
1 |
|
x3 |
|
1 |
– |
|
1 |
1 |
x4 |
1 |
|
1 |
– |
1 |
|
|
x4 |
|
1 |
|
– |
1 |
|
|
x4 |
1 |
1 |
|
– |
|
|
x5 |
|
|
1 |
1 |
– |
|
|
x5 |
1 |
1 |
|
1 |
– |
|
|
x5 |
1 |
|
1 |
|
– |
1 |
x6 |
1 |
1 |
|
|
|
– |
|
x6 |
1 |
|
1 |
|
|
– |
|
x6 |
|
|
1 |
|
1 |
– |
16 17 18
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
|
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
|
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
x1 |
– |
1 |
|
|
1 |
|
|
x1 |
– |
1 |
|
|
|
1 |
|
x1 |
– |
|
1 |
|
|
1 |
x2 |
1 |
– |
|
1 |
|
1 |
|
x2 |
1 |
– |
|
1 |
1 |
|
|
x2 |
|
– |
1 |
1 |
|
1 |
x3 |
|
|
– |
1 |
|
1 |
|
x3 |
|
|
– |
|
1 |
1 |
|
x3 |
1 |
1 |
– |
|
1 |
|
x4 |
|
1 |
1 |
– |
|
|
|
x4 |
|
1 |
|
– |
1 |
1 |
|
x4 |
|
1 |
|
– |
1 |
1 |
x5 |
1 |
|
|
|
– |
1 |
|
x5 |
|
1 |
1 |
1 |
– |
|
|
x5 |
|
|
1 |
1 |
– |
|
x6 |
|
1 |
1 |
|
1 |
– |
|
x6 |
1 |
|
1 |
1 |
|
– |
|
x6 |
1 |
1 |
|
1 |
|
– |
19 20 21
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
|
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
|
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
x1 |
– |
|
1 |
|
1 |
1 |
|
x1 |
– |
1 |
|
1 |
1 |
|
|
x1 |
– |
1 |
|
1 |
1 |
1 |
x2 |
|
– |
1 |
1 |
|
1 |
|
x2 |
1 |
– |
|
|
1 |
|
|
x2 |
1 |
– |
|
1 |
|
|
x3 |
1 |
1 |
– |
1 |
|
|
|
x3 |
|
|
– |
1 |
|
1 |
|
x3 |
|
|
– |
1 |
1 |
|
x4 |
|
1 |
1 |
– |
|
1 |
|
x4 |
1 |
|
1 |
– |
1 |
1 |
|
x4 |
1 |
1 |
1 |
– |
|
|
x5 |
1 |
|
|
|
– |
|
|
x5 |
1 |
1 |
|
1 |
– |
|
|
x5 |
1 |
|
1 |
|
– |
1 |
x6 |
1 |
1 |
|
1 |
|
– |
|
x6 |
|
|
1 |
1 |
|
– |
|
x6 |
1 |
|
|
|
1 |
– |
22 23 24
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
|
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
|
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
x1 |
– |
1 |
1 |
|
|
1 |
|
x1 |
– |
1 |
|
|
|
1 |
|
x1 |
– |
1 |
|
|
1 |
|
x2 |
1 |
– |
|
1 |
|
1 |
|
x2 |
1 |
– |
|
1 |
1 |
|
|
x2 |
1 |
– |
1 |
|
|
1 |
x3 |
1 |
|
– |
1 |
1 |
|
|
x3 |
|
|
– |
1 |
1 |
1 |
|
x3 |
|
1 |
– |
1 |
|
1 |
x4 |
|
1 |
1 |
– |
|
|
|
x4 |
|
1 |
1 |
– |
|
1 |
|
x4 |
|
|
1 |
– |
1 |
|
x5 |
|
|
1 |
|
– |
1 |
|
x5 |
|
1 |
1 |
|
– |
|
|
x5 |
1 |
|
|
1 |
– |
1 |
x6 |
1 |
|
1 |
|
1 |
– |
|
x6 |
1 |
|
1 |
1 |
|
– |
|
x6 |
|
1 |
1 |
|
1 |
– |
25
R |
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
x1 |
– |
|
1 |
|
|
1 |
x2 |
|
– |
1 |
1 |
1 |
|
x3 |
1 |
1 |
– |
|
|
1 |
x4 |
|
1 |
|
– |
|
1 |
x5 |
|
1 |
|
|
– |
1 |
x6 |
1 |
|
1 |
1 |
1 |
– |
Задание 6. Задана таблица покрытий. Построить хотя бы одно кратчайшее покрытие.
1 2
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
|
|
1 |
|
|
|
|
|
|
1 |
|
A |
|
1 |
|
|
|
|
1 |
1 |
|
|
B |
1 |
1 |
|
|
|
|
1 |
|
1 |
|
|
B |
1 |
|
|
1 |
|
|
|
|
|
|
C |
1 |
|
|
1 |
|
1 |
|
|
|
1 |
|
C |
|
|
|
|
|
1 |
|
|
1 |
|
D |
|
|
1 |
1 |
1 |
|
|
|
|
|
|
D |
|
1 |
1 |
|
|
|
|
|
1 |
1 |
E |
|
|
|
|
|
1 |
|
|
1 |
1 |
|
E |
|
|
|
1 |
|
|
|
1 |
|
|
F |
|
|
|
|
|
|
1 |
1 |
|
|
|
F |
1 |
|
|
|
|
1 |
|
|
|
1 |
G |
|
1 |
1 |
|
1 |
|
|
|
|
|
|
G |
|
|
1 |
|
1 |
|
|
|
1 |
|
H |
|
|
|
|
|
1 |
|
1 |
|
|
|
H |
1 |
|
|
|
1 |
1 |
1 |
|
|
|
3 4
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
1 |
1 |
|
|
|
|
|
1 |
|
|
|
A |
|
|
|
1 |
|
1 |
1 |
1 |
|
|
B |
|
1 |
1 |
|
1 |
|
1 |
|
|
|
|
B |
1 |
|
1 |
|
1 |
|
|
|
1 |
|
C |
|
|
|
1 |
|
|
1 |
|
|
|
|
C |
|
|
|
1 |
1 |
1 |
|
|
|
|
D |
|
|
|
1 |
|
|
|
1 |
|
|
|
D |
|
1 |
|
|
|
|
|
|
|
1 |
E |
|
1 |
|
|
|
1 |
|
|
1 |
1 |
|
E |
1 |
|
|
1 |
|
|
|
|
|
|
F |
|
|
1 |
|
|
|
1 |
|
|
1 |
|
F |
|
1 |
1 |
|
|
|
1 |
|
|
|
G |
1 |
|
|
|
1 |
1 |
|
|
1 |
|
|
G |
1 |
|
|
|
|
|
|
1 |
1 |
|
H |
|
|
1 |
|
|
1 |
|
|
|
|
|
H |
|
|
|
|
|
1 |
|
|
|
1 |
5 6
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
|
|
|
1 |
1 |
|
1 |
1 |
|
|
|
A |
|
1 |
|
|
|
|
|
1 |
|
|
B |
|
|
1 |
1 |
|
1 |
|
|
|
|
|
B |
|
|
1 |
|
|
1 |
|
|
|
|
C |
|
1 |
|
|
|
|
|
|
1 |
|
|
C |
1 |
1 |
|
|
1 |
|
|
|
|
|
D |
|
|
|
|
1 |
|
|
1 |
|
1 |
|
D |
|
|
|
1 |
|
|
|
1 |
1 |
|
E |
|
|
1 |
|
|
|
|
1 |
|
|
|
E |
1 |
|
|
1 |
|
|
|
1 |
|
1 |
F |
|
|
|
|
|
1 |
|
|
1 |
|
|
F |
|
|
|
1 |
|
1 |
|
|
|
|
G |
1 |
|
1 |
|
|
1 |
1 |
|
|
|
|
G |
|
1 |
|
|
1 |
|
1 |
|
|
1 |
H |
1 |
1 |
|
|
|
|
|
|
|
1 |
|
H |
|
|
1 |
|
|
|
1 |
|
1 |
|
7 8
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
1 |
|
|
|
|
|
1 |
1 |
|
1 |
|
A |
1 |
|
|
1 |
|
|
|
1 |
|
|
B |
|
|
1 |
1 |
|
|
|
|
|
|
|
B |
1 |
|
1 |
|
|
1 |
|
|
1 |
|
C |
|
|
|
|
1 |
|
|
1 |
1 |
|
|
C |
|
|
|
|
1 |
|
|
1 |
|
|
D |
|
|
|
|
|
1 |
|
|
|
1 |
|
D |
|
1 |
|
|
|
1 |
1 |
|
|
|
E |
|
1 |
1 |
|
1 |
1 |
|
|
|
|
|
E |
|
|
|
|
1 |
|
|
|
1 |
|
F |
1 |
1 |
|
|
|
|
|
|
|
|
|
F |
|
1 |
|
1 |
|
|
|
|
|
|
G |
|
|
|
1 |
|
|
|
|
1 |
|
|
G |
|
|
1 |
1 |
|
|
|
1 |
|
1 |
H |
|
|
1 |
|
|
1 |
1 |
|
|
|
|
H |
|
1 |
|
|
|
|
1 |
|
|
1 |
9 10
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
1 |
|
|
|
1 |
|
|
|
|
|
|
A |
|
|
1 |
1 |
|
|
|
|
|
|
B |
|
1 |
|
1 |
|
1 |
|
|
|
|
|
B |
|
1 |
|
1 |
|
1 |
1 |
|
|
|
C |
1 |
1 |
|
|
|
|
|
1 |
1 |
|
|
C |
|
|
|
|
1 |
1 |
|
|
|
|
D |
|
|
1 |
|
1 |
|
1 |
|
|
|
|
D |
|
1 |
1 |
|
|
|
|
1 |
1 |
|
E |
|
|
1 |
|
1 |
|
|
|
1 |
|
|
E |
1 |
|
|
|
1 |
|
|
|
|
|
F |
1 |
|
|
|
|
1 |
1 |
1 |
|
|
|
F |
|
|
|
1 |
|
1 |
|
|
|
1 |
G |
|
|
|
1 |
|
|
|
|
|
1 |
|
G |
1 |
|
1 |
|
|
|
1 |
1 |
|
|
H |
|
|
1 |
|
|
|
|
|
|
1 |
|
H |
1 |
|
|
|
|
|
|
|
1 |
1 |
11 12
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
1 |
|
|
|
|
|
|
1 |
|
1 |
|
A |
|
|
|
1 |
|
|
|
|
1 |
|
B |
|
1 |
|
|
1 |
|
|
|
|
|
|
B |
|
1 |
|
|
|
|
1 |
|
|
1 |
C |
|
|
|
1 |
|
|
1 |
|
|
|
|
C |
1 |
|
1 |
|
1 |
|
|
|
|
1 |
D |
|
1 |
|
1 |
|
1 |
|
|
|
1 |
|
D |
|
1 |
|
|
|
1 |
1 |
|
|
|
E |
|
|
1 |
|
|
|
1 |
|
1 |
|
|
E |
|
|
1 |
|
|
|
|
|
1 |
|
F |
1 |
|
1 |
|
|
1 |
1 |
|
|
|
|
F |
|
|
|
|
1 |
|
1 |
|
|
|
G |
|
|
|
|
1 |
|
|
1 |
|
|
|
G |
1 |
|
|
1 |
|
|
|
1 |
|
|
H |
|
1 |
|
1 |
|
|
|
|
1 |
|
|
H |
|
|
1 |
|
1 |
1 |
|
1 |
|
|
13 14
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
|
|
1 |
1 |
|
1 |
1 |
|
|
|
|
A |
1 |
|
1 |
|
|
|
1 |
|
|
|
B |
|
1 |
|
|
|
|
|
1 |
1 |
|
|
B |
1 |
|
|
1 |
|
|
|
|
|
|
C |
1 |
|
|
|
|
1 |
|
|
|
1 |
|
C |
|
|
1 |
1 |
|
1 |
|
|
1 |
|
D |
1 |
1 |
|
|
|
|
|
|
1 |
|
|
D |
|
|
|
|
1 |
|
1 |
|
|
|
E |
|
|
|
1 |
|
|
1 |
1 |
|
1 |
|
E |
1 |
|
|
|
|
|
1 |
1 |
|
|
F |
|
|
|
1 |
1 |
|
|
|
|
|
|
F |
|
1 |
|
|
1 |
|
|
|
|
|
G |
|
|
|
|
|
|
1 |
|
1 |
|
|
G |
|
|
|
1 |
|
|
|
1 |
1 |
1 |
H |
|
|
1 |
|
1 |
|
|
|
|
|
|
H |
|
1 |
|
|
|
1 |
|
|
|
1 |
15 16
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
1 |
|
|
|
1 |
1 |
|
|
|
|
|
A |
|
|
1 |
|
1 |
|
|
|
1 |
1 |
B |
|
1 |
|
1 |
|
|
|
|
|
|
|
B |
|
1 |
|
1 |
|
|
|
1 |
|
|
C |
|
|
1 |
|
|
|
|
1 |
1 |
1 |
|
C |
1 |
|
1 |
|
|
|
|
1 |
1 |
|
D |
1 |
|
|
|
|
|
1 |
|
|
|
|
D |
|
1 |
|
|
|
|
1 |
|
|
|
E |
|
|
|
1 |
|
|
|
|
1 |
|
|
E |
1 |
|
|
|
1 |
1 |
|
|
|
|
F |
|
1 |
|
|
1 |
1 |
1 |
|
|
1 |
|
F |
|
1 |
|
1 |
|
|
|
|
|
1 |
G |
|
1 |
1 |
|
|
|
1 |
|
|
|
|
G |
|
|
|
|
|
1 |
1 |
|
|
|
H |
1 |
|
|
|
1 |
|
|
1 |
|
|
|
H |
|
|
|
1 |
|
|
|
|
1 |
|
17 18
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
|
|
1 |
|
|
|
|
1 |
|
1 |
|
A |
1 |
1 |
1 |
|
|
1 |
|
|
|
|
B |
|
1 |
1 |
1 |
|
|
1 |
|
|
|
|
B |
|
|
|
1 |
1 |
|
|
|
|
1 |
C |
|
|
|
1 |
|
1 |
1 |
|
|
1 |
|
C |
|
|
|
|
|
1 |
|
1 |
|
|
D |
1 |
|
|
|
|
1 |
|
|
1 |
|
|
D |
|
1 |
|
|
1 |
1 |
|
|
1 |
|
E |
|
|
|
|
1 |
|
1 |
|
|
|
|
E |
1 |
|
|
|
|
|
1 |
|
1 |
|
F |
1 |
|
|
1 |
|
|
|
|
|
|
|
F |
|
1 |
|
1 |
|
|
|
|
|
|
G |
1 |
1 |
|
|
|
|
|
|
1 |
|
|
G |
|
|
|
|
|
|
1 |
1 |
|
|
H |
|
|
|
|
1 |
|
1 |
|
|
|
|
H |
|
|
1 |
1 |
|
|
|
|
1 |
1 |
19 20
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
1 |
|
1 |
|
|
|
|
|
|
1 |
|
A |
1 |
|
|
|
1 |
1 |
|
|
|
1 |
B |
|
1 |
|
|
1 |
|
|
|
1 |
|
|
B |
|
1 |
1 |
|
|
|
1 |
|
|
|
C |
|
|
1 |
1 |
1 |
|
|
|
|
|
|
C |
|
|
|
|
|
|
|
1 |
1 |
1 |
D |
|
1 |
|
|
|
|
|
|
|
1 |
|
D |
|
|
1 |
|
1 |
1 |
|
1 |
|
|
E |
|
|
|
1 |
|
|
|
1 |
|
|
|
E |
|
|
|
|
|
1 |
1 |
|
|
|
F |
|
1 |
|
|
1 |
1 |
1 |
|
|
|
|
F |
|
|
|
1 |
|
|
|
|
1 |
|
G |
1 |
|
|
|
|
|
1 |
|
1 |
1 |
|
G |
|
|
|
1 |
1 |
|
|
|
|
|
H |
|
|
|
|
|
1 |
|
1 |
|
|
|
H |
1 |
1 |
|
|
|
|
1 |
|
|
|
21 22
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
|
1 |
|
|
1 |
|
|
|
1 |
|
|
A |
|
1 |
|
|
|
|
1 |
1 |
|
1 |
B |
1 |
|
1 |
|
|
|
|
|
|
|
|
B |
|
|
|
|
1 |
|
|
|
1 |
|
C |
|
|
|
|
1 |
|
1 |
|
|
|
|
C |
1 |
|
1 |
1 |
|
|
|
|
|
|
D |
1 |
|
|
|
|
|
|
1 |
|
|
|
D |
|
|
|
1 |
|
|
1 |
|
|
|
E |
|
1 |
1 |
1 |
|
|
1 |
|
|
|
|
E |
|
|
1 |
1 |
|
|
|
1 |
|
|
F |
|
|
|
1 |
|
1 |
|
1 |
|
1 |
|
F |
1 |
1 |
|
|
|
1 |
1 |
|
|
|
G |
|
|
|
|
1 |
|
|
|
1 |
1 |
|
G |
|
|
1 |
|
1 |
|
|
|
|
|
H |
|
|
1 |
|
|
1 |
1 |
|
|
|
|
H |
|
|
|
|
|
1 |
|
|
1 |
1 |
23 24
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
|
|
|
|
|
1 |
|
|
1 |
|
|
A |
1 |
|
|
1 |
1 |
|
1 |
|
|
|
B |
|
1 |
|
|
|
|
|
|
|
1 |
|
B |
|
|
1 |
|
|
|
1 |
|
|
|
C |
|
|
|
1 |
|
1 |
1 |
1 |
|
|
|
C |
1 |
|
|
|
|
1 |
|
|
|
1 |
D |
|
|
1 |
|
|
|
1 |
|
1 |
|
|
D |
|
|
|
|
1 |
|
1 |
1 |
|
|
E |
|
1 |
|
1 |
|
|
|
|
|
|
|
E |
|
1 |
|
1 |
|
|
|
1 |
1 |
|
F |
|
|
|
1 |
1 |
1 |
|
|
|
|
|
F |
|
|
1 |
|
|
|
|
|
|
1 |
G |
1 |
|
1 |
|
|
|
|
|
1 |
|
|
G |
|
1 |
|
|
1 |
|
|
|
|
|
H |
1 |
|
|
|
1 |
|
|
1 |
|
1 |
|
H |
|
1 |
|
|
|
1 |
|
|
1 |
|
25
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
b10 |
A |
|
|
|
1 |
1 |
|
|
1 |
|
1 |
B |
|
|
|
1 |
|
|
1 |
|
|
|
C |
|
|
|
|
|
1 |
1 |
1 |
|
|
D |
1 |
|
1 |
1 |
|
|
|
|
|
1 |
E |
|
1 |
|
|
|
|
|
|
1 |
|
F |
|
|
1 |
|
|
1 |
1 |
|
|
|
G |
1 |
1 |
|
|
1 |
|
|
|
|
|
H |
|
|
|
|
|
1 |
|
|
1 |
|
Задание 7. Задана таблица покрытий. Построить хотя бы одно минимальное покрытие.
1 2
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
A |
|
|
1 |
1 |
|
|
1 |
|
|
1 |
|
A |
|
|
|
1 |
1 |
|
1 |
|
|
1 |
B |
1 |
|
|
|
1 |
|
1 |
|
|
1 |
|
B |
1 |
|
|
|
|
1 |
|
|
1 |
2 |
C |
|
1 |
1 |
1 |
|
|
|
|
1 |
2 |
|
C |
1 |
|
|
1 |
1 |
|
|
1 |
1 |
3 |
D |
|
1 |
|
1 |
1 |
|
1 |
1 |
|
4 |
|
D |
|
|
1 |
|
|
|
|
1 |
1 |
1 |
E |
1 |
|
1 |
|
|
1 |
|
|
1 |
3 |
|
E |
|
1 |
1 |
|
|
1 |
1 |
|
|
3 |
F |
|
|
|
|
1 |
|
|
1 |
1 |
1 |
|
F |
1 |
1 |
|
1 |
|
1 |
1 |
|
|
2 |
G |
|
1 |
|
|
|
1 |
|
1 |
|
2 |
|
G |
|
1 |
|
|
1 |
|
|
1 |
|
2 |
H |
|
|
1 |
|
|
|
|
|
1 |
4 |
|
H |
1 |
|
|
1 |
|
|
|
|
|
4 |
3 4
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
A |
|
1 |
1 |
|
1 |
|
|
1 |
|
3 |
|
A |
|
1 |
|
1 |
|
|
|
1 |
|
2 |
B |
1 |
|
1 |
1 |
|
|
|
1 |
|
2 |
|
B |
|
|
1 |
|
|
1 |
|
|
1 |
1 |
C |
1 |
|
|
1 |
|
1 |
1 |
|
1 |
4 |
|
C |
|
1 |
|
|
1 |
|
1 |
|
1 |
3 |
D |
|
1 |
|
|
|
1 |
|
|
1 |
1 |
|
D |
1 |
|
|
1 |
|
|
1 |
|
1 |
2 |
E |
|
|
1 |
1 |
|
|
|
|
1 |
2 |
|
E |
1 |
|
1 |
|
1 |
|
|
|
|
1 |
F |
1 |
|
|
|
|
|
1 |
1 |
|
2 |
|
F |
1 |
|
1 |
1 |
|
1 |
|
1 |
|
3 |
G |
|
|
|
|
1 |
1 |
1 |
|
|
1 |
|
G |
|
|
1 |
|
|
|
|
|
1 |
2 |
H |
|
|
1 |
|
|
|
|
1 |
|
3 |
|
H |
|
|
|
|
|
1 |
1 |
1 |
|
2 |
5 6
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
A |
|
1 |
|
|
|
|
1 |
1 |
|
1 |
|
A |
1 |
|
|
1 |
1 |
|
|
|
|
2 |
B |
|
|
|
|
|
1 |
|
1 |
1 |
2 |
|
B |
1 |
|
|
1 |
|
1 |
1 |
|
1 |
3 |
C |
|
1 |
1 |
|
1 |
1 |
|
|
|
3 |
|
C |
|
|
|
|
1 |
|
1 |
|
1 |
1 |
D |
|
|
1 |
1 |
|
|
|
|
1 |
2 |
|
D |
|
1 |
|
|
|
1 |
1 |
|
|
2 |
E |
1 |
|
|
|
1 |
|
1 |
|
|
1 |
|
E |
|
1 |
1 |
|
1 |
|
|
1 |
|
3 |
F |
1 |
|
1 |
1 |
|
1 |
|
|
|
2 |
|
F |
1 |
|
1 |
1 |
1 |
|
|
|
|
2 |
G |
|
|
|
|
|
|
1 |
1 |
|
2 |
|
G |
1 |
|
|
|
|
1 |
|
1 |
|
2 |
H |
1 |
|
|
1 |
|
|
1 |
1 |
1 |
3 |
|
H |
|
|
1 |
1 |
|
|
|
|
1 |
1 |
7 8
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
A |
|
|
1 |
|
|
|
|
1 |
|
1 |
|
A |
|
1 |
|
|
|
1 |
|
1 |
|
1 |
B |
|
1 |
|
1 |
|
1 |
|
|
|
2 |
|
B |
|
1 |
|
1 |
|
|
1 |
|
1 |
3 |
C |
1 |
1 |
|
1 |
1 |
|
|
1 |
|
3 |
|
C |
|
|
|
1 |
1 |
|
|
1 |
1 |
2 |
D |
1 |
|
|
1 |
|
1 |
|
|
1 |
2 |
|
D |
|
|
1 |
|
|
1 |
|
|
1 |
2 |
E |
1 |
|
|
|
1 |
|
1 |
|
|
1 |
|
E |
1 |
|
|
|
1 |
|
1 |
|
|
1 |
F |
|
1 |
|
|
1 |
|
|
|
1 |
2 |
|
F |
1 |
|
1 |
1 |
|
|
|
|
|
2 |
G |
|
1 |
|
|
1 |
|
|
1 |
|
4 |
|
G |
|
|
1 |
|
|
1 |
|
|
|
3 |
H |
|
|
1 |
|
|
1 |
1 |
|
1 |
3 |
|
H |
1 |
|
1 |
|
1 |
1 |
|
1 |
|
3 |
9 10
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
A |
1 |
|
|
1 |
|
|
|
|
1 |
2 |
|
A |
1 |
1 |
|
|
|
|
|
1 |
|
1 |
B |
1 |
|
|
|
|
|
1 |
|
1 |
1 |
|
B |
|
1 |
|
1 |
1 |
|
1 |
1 |
|
4 |
C |
1 |
|
1 |
|
|
1 |
|
1 |
|
3 |
|
C |
|
1 |
|
1 |
|
1 |
|
|
|
2 |
D |
|
|
|
|
1 |
|
1 |
1 |
|
2 |
|
D |
|
|
|
|
1 |
1 |
1 |
|
|
1 |
E |
|
1 |
|
1 |
1 |
|
1 |
|
1 |
4 |
|
E |
|
|
1 |
|
|
|
1 |
1 |
|
1 |
F |
|
1 |
1 |
1 |
|
|
|
|
|
1 |
|
F |
1 |
|
1 |
|
|
1 |
|
|
1 |
3 |
G |
|
1 |
|
|
1 |
1 |
|
|
|
1 |
|
G |
|
1 |
|
|
|
|
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11 12
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
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1 |
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1 |
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2 |
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14
R |
b1 |
b2 |
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b5 |
b6 |
b7 |
b8 |
b9 |
с |
|
R |
b1 |
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b8 |
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15 16
R |
b1 |
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b6 |
b7 |
b8 |
b9 |
с |
|
R |
b1 |
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b3 |
b4 |
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b6 |
b7 |
b8 |
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17 18
R |
b1 |
b2 |
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b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
|
R |
b1 |
b2 |
b3 |
b4 |
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с |
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19 20
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
A |
1 |
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1 |
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1 |
2 |
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1 |
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1 |
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3 |
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2 |
21 22
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
A |
1 |
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1 |
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1 |
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1 |
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A |
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1 |
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1 |
1 |
1 |
3 |
B |
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1 |
1 |
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1 |
1 |
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2 |
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1 |
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1 |
2 |
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1 |
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1 |
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3 |
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1 |
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1 |
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1 |
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3 |
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1 |
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1 |
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1 |
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1 |
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1 |
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1 |
23 24
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
|
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
A |
|
|
|
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1 |
|
1 |
|
1 |
1 |
|
A |
|
|
1 |
|
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1 |
|
|
1 |
2 |
B |
1 |
|
1 |
|
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1 |
|
|
1 |
3 |
|
B |
1 |
|
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1 |
|
1 |
1 |
|
2 |
C |
|
|
1 |
1 |
|
1 |
|
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2 |
|
C |
|
1 |
1 |
1 |
|
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1 |
D |
1 |
1 |
|
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1 |
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1 |
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D |
1 |
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1 |
1 |
|
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1 |
3 |
E |
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1 |
1 |
|
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1 |
|
2 |
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E |
|
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1 |
1 |
|
1 |
|
2 |
F |
|
1 |
|
1 |
1 |
|
1 |
1 |
|
3 |
|
F |
1 |
1 |
|
|
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1 |
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1 |
G |
|
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1 |
1 |
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1 |
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1 |
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G |
|
1 |
1 |
|
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1 |
1 |
1 |
|
3 |
H |
|
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1 |
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1 |
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3 |
|
H |
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1 |
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1 |
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|
2 |
25
R |
b1 |
b2 |
b3 |
b4 |
b5 |
b6 |
b7 |
b8 |
b9 |
с |
A |
|
|
1 |
|
1 |
|
|
|
1 |
1 |
B |
1 |
|
|
1 |
|
|
|
|
1 |
2 |
C |
|
1 |
|
|
|
|
1 |
1 |
|
1 |
D |
1 |
|
1 |
|
1 |
|
|
1 |
|
2 |
E |
1 |
|
1 |
|
|
1 |
1 |
|
|
3 |
F |
|
1 |
|
1 |
1 |
|
|
1 |
1 |
3 |
G |
|
1 |
|
1 |
|
1 |
|
|
|
2 |
H |
1 |
|
|
|
1 |
|
|
1 |
|
3 |
Задание 8. Найти кратчайшее и минимальное покрытия (задания 6 и 7), используя метод ветвей и границ.