
Математические основы теории систем.-1
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5. (a* bc)* a
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Вариант № 3
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5. (b* ac*)* (b a)
x = x1x2x2x1x3x2x1
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x = x2x1x2x1x2x3x3
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Вариант № 4
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5. (a* b ca) b*
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Вариант № 5
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x = x3x3x2x2x1x1x1
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52

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5. (ac* b c) ac
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Вариант № 6
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x = x1x2x1x2x3x3x3
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x = x1x2x1x1x2x3x3
53

5. (c b* a)* a*
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3 3 2 4
4− 4 −
Вариант № 7
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5. (bc*)* b a |
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Вариант № 8
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x = x1x1x1x2x3x3x3
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5. (ca ba*)* (b c)* |
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Вариант № 9
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x = x3x2x1x3x2x1x1
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x = x1x1x1x2x2x2x3
55

5. (a b)* c* ba
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1 − 2 4
6. 2 3 4 −
3 2 3 4
4− − 4
Вариант № 10
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5. (a c*) b* (ac)* |
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Вариант № 11
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qi x j |
x 1 |
x 2 |
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1. |
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3, y 1 |
3, y 1 |
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2 |
1, y 2 |
3, y 1 |
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3 |
1, y 1 |
2 , y 2 |
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qi |
x j |
x1 |
x 2 |
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2. |
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1 |
2 , y 1 |
1, y 1 |
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2 |
1, y 2 |
2 , y 3 |
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x = x1x2x3x2x3x1x2
qi |
x j |
x 1 |
x 2 |
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2. |
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1 |
1, y 2 |
2 , y 3 |
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2 |
1, y 1 |
1, y 2 |
56

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3. |
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y 1 |
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x 3 |
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4 , y 2 |
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2 , y 1 |
3, y 1 |
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4. |
2 |
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3, y 2 |
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1, y 1 |
4 , y 2 |
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2 , y 2 |
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1, y 2 |
4 , y 1 |
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1, y 2 |
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5. (a* c) b* c* a |
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6. |
2 |
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4 |
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3 2 3 4
44 2 −
Вариант № 12.
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qi |
x j |
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x1 |
x 2 |
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1. |
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1 |
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1, y 2 |
3, y 2 |
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2 |
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1, y 1 |
3, y 1 |
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3 |
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2 , y 2 |
1, y 1 |
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x 2 |
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4 |
2 |
y 3 |
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3. 2 |
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3 |
4 |
y 2 |
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3 |
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2 |
1 |
y 1 |
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4 |
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3 |
2 |
y 1 |
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x 3 |
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1 |
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2 , y 1 |
4 , y 1 |
2 , y 2 |
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4. 2 |
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3, y 1 |
4 , y 2 |
1, y 1 |
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3 |
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4 , y 2 |
3, y 2 |
1, y 2 |
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4 |
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3, y 1 |
4 , y 2 |
2 , y 1 |
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x = x1x1x2x1x1x3x2
qi |
x j |
x 1 |
x 2 |
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2. |
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1 |
2 , y 1 |
1, y 3 |
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2 |
1, y 2 |
2 , y 2 |
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x = x1x2x2x1x2x3x2
57

5. (b (ac)*) ab*
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q |
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b |
c |
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1 |
3 |
− |
4 |
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6. |
2 |
2 |
1 |
4 |
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3 |
4 |
1 |
2 |
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4 |
− |
4 |
4 |
Вариант № 13
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qi |
x j |
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x 1 |
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x 2 |
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1. |
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1 |
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2 , y 1 |
3, y 1 |
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2 |
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2 , y 1 |
1, y 2 |
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3 |
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2 , y 1 |
3, y 1 |
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x1 |
x2 |
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3 |
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y 2 |
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3. |
2 |
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2 |
4 |
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y1 |
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3 |
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1 |
2 |
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y 4 |
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2 |
1 |
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y 3 |
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q |
x |
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x1 |
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x 2 |
x 3 |
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1 |
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3, y 2 |
2 , y 1 |
4 , y 1 |
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4. 2 |
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3, y 1 |
4 , y 1 |
1, y 2 |
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3 |
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2 , y 2 |
3, y 1 |
4 , y 2 |
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4 |
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1, y 2 |
2 , y 2 |
3, y 1 |
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5. (c ab)* c* |
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q |
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a |
b |
c |
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1 |
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3 |
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2 |
1 |
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6. |
2 |
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− |
4 |
− |
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3 |
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2 |
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4 |
− |
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4 |
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2 |
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− |
4 |
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Вариант № 14
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qi x j |
x 1 |
x 2 |
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1. |
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1 |
3, y 1 |
1, y 1 |
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2 |
1, y 1 |
3, y 1 |
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3 |
2 , y 1 |
1, y 2 |
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qi |
x j |
x1 |
x 2 |
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2. |
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1 |
1, y 2 |
2 , y 2 |
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2 |
2 , y 1 |
1, y 3 |
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x = x2x1x2x1x2x3x2
qi |
x j |
x1 |
x 2 |
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2. |
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1 |
2 , y 3 |
2 , y 2 |
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2 |
1, y 1 |
2 , y 2 |
58

q |
x |
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x1 |
x 2 |
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1 |
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2 |
3 |
y 1 |
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3. |
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2 |
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1 |
2 |
y 2 |
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3 |
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4 |
3 |
y 3 |
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4 |
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1 |
3 |
y 1 |
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q |
x |
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x 1 |
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x 2 |
x 3 |
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1 |
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4 , y 1 |
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2 , y 2 |
3, y 1 |
4. 2 |
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1, y 2 |
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3, y 1 |
4 , y 2 |
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3 |
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2 , y 1 |
3, y 2 |
1, y 2 |
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4 |
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3, y 1 |
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1, y 1 |
4 , y 2 |
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5. (a* b)* (a c) b*
q |
a |
b |
c |
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1 |
4 |
3 |
3 |
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6. 2 |
3 |
− |
4 |
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3 |
3 |
2 |
− |
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4 |
4 |
− |
− |
Вариант № 15
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qi |
x j |
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x1 |
x 2 |
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1. |
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1 |
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1, y 1 |
1, y 2 |
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2 |
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1, y 1 |
3, y 2 |
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3 |
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2 , y 1 |
1, y 2 |
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q |
x |
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x1 |
x 2 |
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1 |
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1 |
2 |
y 2 |
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3. 2 |
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3 |
4 |
y 2 |
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3 |
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2 |
1 |
y 3 |
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4 |
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3 |
2 |
y 1 |
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q |
x |
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x1 |
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x 2 |
x 3 |
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1 |
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1, y 1 |
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2 , y 1 |
4 , y 2 |
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4. 2 |
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1, y 2 |
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3, y 1 |
2 , y 1 |
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3 |
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4 , y 1 |
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1, y 2 |
1, y 1 |
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4 |
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3, y 1 |
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2 , y 2 |
1, y 2 |
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x = x1x3x1x3x2x2x2
qi |
x j |
x1 |
x 2 |
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2. |
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1 |
1, y 3 |
2 , y 4 |
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2 |
1, y 1 |
1, y 2 |
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x = x2x2x1x2x3x2x2
59

5. (c ba)(c* a*)*
q |
a |
b |
c |
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1 |
4 |
− |
3 |
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6. 2 |
2 |
4 |
− |
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3 |
2 |
− |
2 |
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4 |
− |
4 |
− |
Вариант № 16
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qi |
x j |
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x1 |
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x 2 |
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1. |
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1 |
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3, y 1 |
2 , y 2 |
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2 |
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1, y 2 |
3, y 1 |
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3 |
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3, y 2 |
1, y 2 |
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q |
x |
x1 |
x2 |
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1 |
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4 |
3 |
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y 4 |
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3. |
2 |
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2 |
1 |
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y1 |
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3 |
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3 |
2 |
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y 2 |
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4 |
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1 |
3 |
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y 3 |
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q |
x |
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x1 |
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x 2 |
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x 3 |
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1 |
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2 , y 1 |
4 , y 2 |
2 , y 2 |
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4. 2 |
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3, y 1 |
1, y 2 |
4 , y 1 |
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3 |
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3, y 2 |
2 , y 1 |
1, y 2 |
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4 |
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1, y 2 |
3, y 2 |
2 , y 1 |
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5. (a b)* c* a |
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q |
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a |
b |
c |
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1 |
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− |
4 |
3 |
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6. |
2 |
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2 |
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3 |
4 |
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3 |
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3 |
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2 |
− |
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4 |
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4 |
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− |
4 |
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Вариант № 17
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qi x j |
x1 |
x 2 |
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1. |
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1 |
2 , y 1 |
3, y 1 |
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2 |
3, y 2 |
1, y 1 |
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3 |
1, y 1 |
3, y 2 |
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qi |
x j |
x 1 |
x 2 |
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2. |
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1 |
1, y 1 |
2 , y 4 |
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2 |
1, y 2 |
1, y 3 |
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x = x3x3x2x1x2x2x2
qi |
x j |
x 1 |
x 2 |
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2. |
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1 |
1, y 3 |
1, y 2 |
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2 |
2 , y 1 |
1, y 3 |
60