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, , . , . , : 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 Cxi, . 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 1x 2x 3 V x 1x 2& x 3 V x 1& x 2& x 3.

2. 4 ( C = 6) , , :

Ø x 1& x 2& x 3V x 1& x 2& x 3 = x 2& x 3.

x 1x 2x 3 V x 1x 2& x 3 = x 1x 2.

x 1x 2& x 3 V x 1& x 2& x 3 = x 1& x 3.

, 3 :

x 2& x 3, x 1x 2, x 1& x 3.

.

3 ( 3) , .

f:

F 1(x 1, x 2, x 3) = x 2& x 3 V x 1x 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 1x 2x 3 V x 1x 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.

.

. . , R. , R , , , , , . .

. R :

(1 0 );

( 1 1);

(1 1).

:

f (x 1, x 2, x 3) = x 2& x 3 V x 1x 2 V x 1& x 3.

.

4.14. () , , .

.

4.15. , A , , .. .

4.19.

x 1x 2 x 1x 2& x 3 x 1x 2x 3, x 1& x 2& x 3 Ø x 1x 2x 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. .

, , ( , ), , , , .

4. .

3, , , , , , . . .

5. .

(. . ), ( ). .

4.20.

.

1. . , :

f (x 1, x 2, x 3) = Ø x 1& x 2& x 3V x 1x 2x 3 V x 1x 2& x 3 V x 1& x 2& x 3

:

F 1(x 1, x 2, x 3) = x 2& x 3 V x 1x 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 1x 3 ( 2- ) . : x 1x 2x 3 x 1x 2& x 3 ( 2- 3- ).

(1- 2-) (1-, 2-, 3- 4-) . . , x 2& x 3 x 1x 3 .

, :

F 2(x 1, x 2, x 3) = x 2& x 3 V x 1x 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 1x 2& x 3& x 4 V Ø x 1& x 2x 3 & x 4 V Ø x 1& x 2x 3x 4 V

Ø x 1& x 2& x 3& x 4V x 1x 2x 3& x 4V x 1x 2& x 3& x 4V x 1& x 2x 3x 4V x 1& x 2x 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 1x 2& x 4 V x 1x 3& x 4 x 2x 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 2x 3 ( 6- ), . : Ø x 1& x 2x 3& x 4, Ø x 1& x 2x 3x 4, x 1& x 2x 3x 4, x 1& x 2x 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 1x 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 1x 2& x 4 V x 2x 3 .

 





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