2.1. á. , - á, , , - , , -.
1. x, y, z :
r 1: x y z;
r 2: x z y;
r 3: y x z.
x 1 1- 2- 2 3- . - S (x) = 1+1+2 = 4. y 2 1- , 3 2- 1 3- , .. S (y) = 2+3+1 = 6. , z 3 1- 3- 2 2- , .. S (z) = 3+2+3 = 8. , , r: x y z ■
, 1 , á, , .., , . .
2. x, y, z, w, :
r 1: w x y z;
r 2: w z x y;
r 3: w y z x.
. wS (w) = 3. - x S (x) = 2+3+4 = 9. S (y) = 3+4+2 = 9 S (z) = 3+2+3 = 9. , r: { w } { x, y, z } ■
3.
r 1: x y z;
r 2: y z x;
r 3: z x y
S (x) = S (y) = S (z) = 6. , 1, { x, y, z }. { x, y, z } , , ■
- , 2.2 2.4
1. , á, -:
01 r 1: x 1 x 2 x 3 x 4; r 2: x 2 x 4 x 1 x 3; r 3: x 1 x 3 x 2 x 4. | 02 r 1: x 1 x 3 x 4 x 2; r 2: x 2 x 4 x 1 x 3; r 3: x 3 x 1 x 2 x 4. | 03 r 1: x 2 x 1 x 3 x 4; r 2: x 2 x 4 x 1 x 3; r 3: x 1 x 3 x 2 x 4. |
04 r 1: x 2 x 3 x 5 x 4; r 2: x 2 x 4 x 1 x 3; r 3: x 3 x 1 x 2 x 4. | 05 r 1: x 1 x 2 x 4 x 3; r 2: x 2 x 4 x 3 x 1; r 3: x 1 x 3 x 2 x 4. | 06 r 1: x 1 x 4 x 2 x 3; r 2: x 2 x 1 x 4 x 3; r 3: x 3 x 1 x 2 x 4. |
07 r 1: x 2 x 1 x 4 x 3; r 2: x 1 x 4 x 2 x 3; r 3: x 1 x 3 x 2 x 4. | 08 r 1: x 2 x 4 x 3 x 5; r 2: x 2 x 4 x 1 x 3; r 3: x 1 x 3 x 2 x 4. | 09 r 1: x 1 x 3 x 2 x 4; r 2: x 2 x 4 x 1 x 3; r 3: x 3 x 1 x 2 x 4. |
10 r 1: x 1 x 3 x 2 x 4; r 2: x 2 x 4 x 1 x 3; r 3: x 3 x 1 x 2 x 4. | 11 r 1: x 1 x 3 x 2 x 4; r 2: x 2 x 1 x 4 x 3; r 3: x 2 x 1 x 3 x 4. | 12 r 1: x 1 x 2 x 3 x 4 x 5; r 2: x 3 x 5 x 1 x 2 x 4; r 3: x 2 x 1 x 4 x 5 x 3. |
13 r 1: x 1 x 2 x 3 x 5 x 4; r 2: x 3 x 5 x 1 x 2 x 4; r 3: x 2 x 4 x 1 x 5 x 3. | 14 r 1: x 1 x 2 x 4 x 3 x 5; r 2: x 2 x 5 x 1 x 3 x 4; r 3: x 2 x 1 x 4 x 5 x 3. | 15 r 1: x 1 x 2 x 4 x 5 x 3; r 2: x 3 x 4 x 1 x 2 x 5; r 3: x 2 x 1 x 4 x 5 x 3. |
16 r 1: x 1 x 2 x 5 x 3 x 4; r 2: x 3 x 5 x 1 x 2 x 4; r 3: x 2 x 1 x 4 x 5 x 3. | 17 r 1: x 1 x 2 x 5 x 4 x 3; r 2: x 3 x 5 x 1 x 2 x 4; r 3: x 2 x 1 x 4 x 5 x 3. | 18 r 1: x 1 x 3 x 2 x 4 x 5; r 2: x 3 x 5 x 1 x 4 x 2; r 3: x 2 x 1 x 4 x 5 x 3. |
19 r 1: x 1 x 3 x 2 x 5 x 4; r 2: x 3 x 5 x 1 x 2 x 4; r 3: x 2 x 1 x 4 x 5 x 3. | 20 r 1: x 1 x 3 x 4 x 2 x 5; r 2: x 2 x 5 x 1 x 3 x 4; r 3: x 2 x 1 x 4 x 5 x 3. | 21 r 1: x 1 x 3 x 4 x 5 x 2; r 2: x 3 x 5 x 1 x 2 x 4; r 3: x 2 x 1 x 4 x 5 x 3. |
22 r 1: x 1 x 3 x 5 x 4 x 2; r 2: x 3 x 5 x 1 x 2 x 4; r 3: x 2 x 4 x 1 x 5 x 3. | 23 r 1: x 5 x 1 x 4 x 3 x 2; r 2: x 1 x 5 x 3 x 4 x 2; r 3: x 4 x 1 x 2 x 5 x 3; r 4: x 5 x 4 x 1 x 3 x 2. | 24 r 1: x 5 x 1 x 4 x 2 x 3; r 2: x 1 x 5 x 3 x 4 x 2; r 3: x 4 x 1 x 2 x 5 x 3; r 4: x 5 x 1 x 3 x 4 x 2. |
25 r 1: x 5 x 1 x 3 x 4 x 2; r 2: x 1 x 5 x 3 x 4 x 2; r 3: x 4 x 1 x 5 x 2 x 3; r 4: x 5 x 1 x 3 x 4 x 2. | 26 r 1: x 5 x 1 x 3 x 2 x 4; r 2: x 1 x 5 x 3 x 4 x 2; r 3: x 4 x 1 x 2 x 3 x 5; r 4: x 5 x 1 x 3 x 4 x 2. | 27 r 1: x 5 x 1 x 2 x 3 x 4; r 2: x 1 x 5 x 2 x 4 x 3; r 3: x 4 x 1 x 2 x 5 x 3; r 4: x 5 x 1 x 3 x 4 x 2. |
28 r 1: x 5 x 1 x 2 x 4 x 3; r 2: x 1 x 5 x 2 x 3 x 4; r 3: x 4 x 1 x 2 x 5 x 3; r 4: x 5 x 1 x 3 x 4 x 2. | 29 r 1: x 5 x 3 x 1 x 2 x 4; r 2: x 1 x 5 x 3 x 4 x 2; r 3: x 4 x 1 x 2 x 5 x 3; r 4: x 5 x 1 x 3 x 4 x 2. | 30 r 1: x 5 x 3 x 1 x 4 x 2; r 2: x 1 x 5 x 3 x 4 x 2; r 3: x 4 x 1 x 2 x 5 x 3; r 4: x 5 x 1 x 3 x 4 x 2. |
31 r 1: x 5 x 3 x 2 x 1 x 4; r 2: x 1 x 5 x 3 x 4 x 2; r 3: x 4 x 1 x 5 x 2 x 3; r 4: x 5 x 1 x 3 x 4 x 2. | 32 r 1: x 5 x 3 x 2 x 4 x 1; r 2: x 1 x 5 x 3 x 4 x 2; r 3: x 4 x 1 x 2 x 3 x 5; r 4: x 5 x 1 x 3 x 4 x 2. | 33 r 1: x 5 x 3 x 4 x 1 x 2; r 2: x 1 x 5 x 3 x 4 x 2; r 3: x 4 x 1 x 2 x 5 x 3; r 4: x 5 x 1 x 3 x 4 x 2. |
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2.2. . , , n m , Ω. x v (x) = (v 1(x), , vn (x)), vi (x) , x i - (i = 1, , n). - R Ω : xRy -, v (x) v (y) ( ). , R Ω , .. 14-2.3 . Ω 1 ΩR R , Ω 2 = (Ω Ω 1) R, .. Ω 1 1, Ω 2 2, .. ( , ).
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4. 3 5 :
r 1: x 1 x 3 x 4 x 2 x 5;
r 2: x 2 x 5 x 1 x 3 x 4;
r 3: x 2 x 1 x 4 x 5 x 3.
v (x). , v (x 1) = (1,3,2), v (x 2) = (4,1,1), v (x 3) = (2,4,5), v (x 4) = (3,5,3), v (x 5) = (5,2,4). , v (x 3) v (x 4) v (x 1), v (x 5) v (x 2), v (x 1) v (x 2) . Ω 1 = { x 1, x 2}. v (x 3) = (2,4,5), v (x 4) = (3,5,3), v (x 5) = (5,2,4) . : { x 1, x 2} { x 3, x 4 , x 5}.
, á. : S (x 1) = 6, S (x 2) = 6, S (x 3) = 11, S (x 4) = 11, S (x 5) = 11, .. . , , á , ■
5. 5 :
r 1: x 1 x 2 x 3 x 4 x 5;
r 2: x 1 x 2 x 3 x 4 x 5;
r 3: x 2 x 3 x 4 x 5 x 1.
: { x 1, x 2} { x 3} { x 4} { x 5}. á : S (x 1) = 7, S (x 2) = 5, S (x 3) = 8, S (x 4) = 11, S (x 5) = 14. : x 2 x 1 x 3 x 4 x 5, , ■
2. 1, ■
2.3. ( ). - . .
6. . 5 , Ω:
r 1: x 5 x 3 x 2