, , . , . , : f 1(x 1, x 2) = x 1V x 1& x 2 V Ø x 2 f 2(x 1, x 2) = x 1 V Ø x 2 , 2- ( 6 4.3) x 1 V x 1& x 2 º x 1.
f 1(x 1, x 2) , f 2(x 1, x 2) .
4.10. , .
4.11. f (x 1, x 2,..., xn) , 0, C V f f. , ( 5) .
4.12. C f , C , f.
4.17.
x & y V x & z V x & y & z º x &(y V z) x & y x & z , x & y & z , .
4.13. f f.
, .
4.5. ( ).
1. f F, .
2. f. F . , C & xi C &Ø xi, . 1- () ( 7). n - 1 . , , . , n - 1 , , , , , n - 2 , n - 1 . . , . . F 1, F, , .. .
4.18.
4.4:
f (x 1, x 2, x 3) = Ø(x 2 Ø x 3) ~(Ø x 1V x 2).
1. 1 (. 4.13, 4.15). f (x 1, x 2, x 3)
F (x 1, x 2, x 3) = Ø x 1& x 2& x 3V x 1&Ø x 2&Ø x 3 V x 1&Ø x 2& x 3 V x 1& x 2& x 3.
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2. 4 ( C = 6) , , :
Ø x 1& x 2& x 3V x 1& x 2& x 3 = x 2& x 3.
x 1&Ø x 2&Ø x 3 V x 1&Ø x 2& x 3 = x 1&Ø x 2.
x 1&Ø x 2& x 3 V x 1& x 2& x 3 = x 1& x 3.
, 3 :
x 2& x 3, x 1&Ø x 2, x 1& x 3.
.
3 ( 3) , .
f:
F 1(x 1, x 2, x 3) = x 2& x 3 V x 1&Ø x 2 V x 1& x 3.
-. . .
4.6. ( - - ).
1. ( , 4.3 )
4.4.
, 4. 3 (. 4.15), :
f (x 1, x 2, x 3) = Ø x 1& x 2& x 3V x 1&Ø x 2&Ø x 3 V x 1&Ø x 2& x 3 V x 1& x 2& x 3.
2. , 1, , . Ai , , i , , .
A 0 ( , 1) .
A 1 ( , , 1):
1 0 0
A 2:
0 1 1
1 0 1
A 3:
1 1 1
3. , . , , , (). , . : ( P) ( R).
.
A 1 A 2:
(1 0 0) (1 0 1) (1 0 );
A 2 A 3:
(0 1 1) (1 1 1) ( 1 1);
(1 0 1) (1 1 1) (1 1);
R , . . , P = P (1) :
(1 0 );
( 1 1);
(1 1).
. . , . , ( ). , . , , R.
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.
. . , R. , R , , , , , . .
. R :
(1 0 );
( 1 1);
(1 1).
:
f (x 1, x 2, x 3) = x 2& x 3 V x 1&Ø x 2 V x 1& x 3.
.
4.14. () , , .
.
4.15. , A , , .. .
4.19.
x 1&Ø x 2 x 1&Ø x 2& x 3 x 1&Ø x 2&Ø x 3, x 1& x 2& x 3 Ø x 1&Ø x 2&Ø x 3.
, . , . . 4.15 .
.
4.7. ( ).
1. .
f (x 1, x 2,..., xn) = Ai º Bj, m k,
Ai , , i = 1, 2,..., k, k n, Bj , j = 1, 2,..., m, m k, , , . - , (, * ).
2. , .
- , , , , , . . . . , , , .
3. .
, , ( , ), , , , .
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4. .
3, , , , , , . . .
5. .
(. . ), ( ). .
4.20.
.
1. . , :
f (x 1, x 2, x 3) = Ø x 1& x 2& x 3V x 1&Ø x 2&Ø x 3 V x 1&Ø x 2& x 3 V x 1& x 2& x 3
:
F 1(x 1, x 2, x 3) = x 2& x 3 V x 1&Ø x 2 V x 1& x 3.
x 1 s 1& x 2 s 2&...& xnsn, (xi si = xi, si = 0 xisi = Ø xi, si = 1, i = 1, 2,..., n), , . . , , 0 , , 1 , . ( 4.6) 4 , 4 F (x 1, x 2, x 3, x 4) 3 , 3 F 1(x 1, x 2, x 3, x 4).
4.6
11 | * | * | ||
10 | * | * | ||
11 | * | * |
2. , 1- 2- . x 2& x 3 ( 1- ) . : Ø x 1& x 2& x 3 x 1& x 2& x 3 ( 1- 4- ). x 1&Ø x 3 ( 2- ) . : x 1&Ø x 2&Ø x 3 x 1&Ø x 2& x 3 ( 2- 3- ).
(1- 2-) (1-, 2-, 3- 4-) . . , x 2& x 3 x 1&Ø x 3 .
, :
F 2(x 1, x 2, x 3) = x 2& x 3 V x 1&Ø x 2 .
.
4.21.
4.7
x 1 x 2 x 3 x 4 | f (x 1, x 2, x 3, x 4) |
0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 |
- - .
, 4.3, :
F (x 1, x 2, x 3, x 4) = Ø x 1&Ø x 2& x 3& x 4 V Ø x 1& x 2 &Ø x 3 & x 4 V Ø x 1& x 2&Ø x 3&Ø x 4 V
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Ø x 1& x 2& x 3& x 4V x 1&Ø x 2&Ø x 3& x 4V x 1&Ø x 2& x 3& x 4V x 1& x 2&Ø x 3&Ø x 4V x 1& x 2&Ø x 3& x 4.
, 1, , .
A 0 .
A 1:
0 1 0 0
A 2:
0 0 1 1
0 1 0 1
1 0 1 0
1 1 0 0
A 3:
0 1 1 1
1 0 1 1
1 1 0 1
A 4 .
, .
A 1 A 2:
(0 1 0 0) (0 1 0 1) (0 1 0 );
(0 1 0 0) (1 1 0 0) ( 1 0 0);
A 2 A 3:
(0 0 1 1) (0 1 1 1) (0 1 1);
(0 0 1 1) (1 0 1 1) ( 0 1 1);
(0 1 0 1) (0 1 1 1) (0 1 1);
(0 1 0 1) (1 1 0 1) ( 1 0 1);
(1 0 0 1) (1 0 1 1) (1 0 1);
(1 0 0 1) (1 1 0 1) (1 0 1);
(1 1 0 0) (1 1 0 1) (1 1 0 ).
R , . . , P = P (1) :
(0 1 0 );
( 1 0 0);
(0 1 1);
( 0 1 1);
(0 1 1);
( 1 0 1);
(1 0 1);
(1 0 1);
(1 1 0 ).
. , , R.
(0 1 0 ) (1 1 0 ) ( 1 0 );
( 1 0 0) ( 1 0 1) ( 1 0 )
R , :
(0 1 1);
( 0 1 1)
(0 1 1);
(1 0 1);
(1 0 1);
P (2) :
( 1 0 ).
. P (2) R, :
(0 1 1);
( 0 1 1)
(0 1 1);
(1 0 1);
(1 0 1);
( 1 0 ).
:
F 1(x 1, x 2, x 3, x 4) = Ø x 1& x 3& x 4 V Ø x 2& x 3& x 4 V Ø x 1& x 2& x 4 V x 1&Ø x 2& x 4 V x 1&Ø x 3& x 4 x 2&Ø x 3.
( 4.7).
.
( 4.8) 8 , 8 F (x 1, x 2, x 3, x 4) 6 , 6 F 1(x 1, x 2, x 3, x 4).
4.8
0-11 | * | * | ||||||
-011 | * | * | ||||||
01-1 | * | * | ||||||
10-1 | * | * | ||||||
1-01 | * | * | ||||||
-10- | * | * | * | * |
, 2- 7- . x 2&Ø x 3 ( 6- ), . : Ø x 1& x 2&Ø x 3& x 4, Ø x 1& x 2&Ø x 3&Ø x 4, x 1& x 2&Ø x 3&Ø x 4, x 1& x 2&Ø x 3& x 4 ( 2-, 3 - , 7 - 8 - ). . :
4.9
0-11 | * | * | ||
-011 | * | * | ||
01-1 | * | |||
10-1 | * | * | ||
1-01 | * |
. . , . Ø x 1& x 3& x 4 x 1&Ø x 2& x 4 (1 - 4 - 4. 9), . . .
, :
F 2(x 1, x 2, x 3, x 4) = Ø x 1& x 3& x 4 V x 1&Ø x 2& x 4 V x 2&Ø x 3 .
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