1. ()
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, : (0) (1). .

, , , , (1815-1864), .

, , . 1, 0.

, , . , , A, B, C, , F, , , .

:

  1. ( ). F = A /\ B, F = A·B, F = AB, A B. , , .
  2. ( ). F = A \/ B, F = A+B, F = A B. , , , , .
  3. ( ). F = Ā , F = A. , , , .

(. 1) :

1

( )

( )

A /\ B

A \/ B

0

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, . , , , , , . , , (. 2) .

                                                   

. 2. : (), (), ()

: ( A↓B), ( A│B), .

, -.

. , , .

, (. 3).

. 3.

, , .

, , .

- , , .

X(x1 xn), Y(y1 yk),. .

.

Y X . .

Y X, , . , .

. 4.

         

. 4.

, , , .

, , .

y1 = y1 (x1 , x2 , , xn),

yk = yk (x1 , x2 , , xn).

yi xm , , .

, , . .

yi t+1 = fi (x1 , x2 , , xn , z1 , z2 , , zs)t+1.

.

, ..

yi t+1 = fi (z1 , z2 , , zs)t+1.

.

.

. - . . xm , , . . . . , - . . , .

. . , , () , . , , , .. , . , .

, , .

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, :

0 0 = 0 1 · 1 = 1

0 1 = 1 1 · 0 = 0

1 0 = 1 0 · 1 = 0

1 1 = 1 0 · 0 = 0

, , . .

, :

, .

, , :

; .

, , , .

, , , , () , (), (). , .

.

:

A 0 = A4. A Ā = 17. A · A = A

2. A 1 = 15. A · 0 = 08. A · Ā = 0

3. A A = A6. A · 1 = 19.

:

10. ) A B = B A, ) AB = BA

, , .

11. ) A B C = A (B C) = (A B) C,

) ABC = A(BC) = (AB)C .

12. ) A (B C) = AB AC, ) A BC = (A B)(A C)

.

. 12, :

,

.

: , : , 12, .

13. ) A AB = A, ) A(A B) = A

(A B).

13, :

A AB = A(1 B) = A · 1 = A, ( 2, 6).

13, .

14. ) , ) .

14.:

, ( 8 1).

14, .

15. ) AB ĀB = B, į) (A B)(Ā B) = B, ( A).

15, :

AB ĀB = B(A Ā) = B · 1 = B, (čń 4 6).

15, .

()

(F) (A, B, C, ) .

(0 1) .

, N 2N .

, , . , , . ( ).

: , , , .

.

F1 A, B, C 1, ( ) 1. . 23 = 8.

F2 A, B, C 1, 1, , .

0 23 1, (. 1).

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A

B

C

F1

F2

F3

F4

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F 2 0 7 , , 1 .

F3 F4 .

(F3) n , , , . .

(F4) n , , , .

, : , , .

, ( ) , , .

, , , , .

F1 :

.

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, , , , .

F1 :

.

. , .

, . , . , .. .

.

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, ( , ).

, , , .

, , F1 , :

, . . , , ( ).

, .

: , , . , .

.

AC. AC = 1, A = 1 C = 1. A = 1 C = 1,

.

B = 0 F(A, B, C) = 11 00 = 1, F(A, B, C) = 01 00 = 0. , AC .

BC, 1 B = 0, C = 1.

.

1 A = 1, A = 0. .

, , :

.

( ) , .

, , , . . 2n. , , , .

, . , (. 5)

, , . , ( ) . .

, :

. 5 Ā (.. ) Ā). B, . , F(A,B) = Ā B.

, , .

, , ,

.

, 23 = 8 , , . 6.

, -, . , , - .

.

, . , , , , .

, (. 7).

(. 7, ), :

.

(. 7, ), (, j )

.

j , F , F , .

, , .

. : , , .

, .

Ȗ, Ȗ

- -. .

.

.

, F -, - (. 8)

. 8. -

, -.


, 1990- CMB ( ), 1974. , . FAQ .


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