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, .
1. 0 0 = 0; 1 1 = 1; 0 1 = 1 0 = 0;
2. 0 v 0 = 0; 1 v 1 = 1; 0 v 1 = 1 v 0 = 1;
3. x = 0, = 1;
x = 1, = 0;
5 . , . , 2 - 0 1.
4. :
5. (, ):
n :
6. :
7. " ":
8. ():
4 .
9. ( ):
10. ( ):
11. ( ):
:
:
12. ( ):
-:
3 , " ".
13. ():
14. -:
15. ():
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( ) (), " v ", (), " & ", " " , (), (" - ") , , . , .
|
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- () () , . , x1x2x3, 1x3.
() - . "" , , . .
f = x1x2x3 v 1x3.
() , , , , ( ).
- () () , . , (x1 v x2 v x3), ( 1 v x3).
() - . "" , , . . f = (x1 v x2 v x3) ( 1 v x3).
() , , , , ( ).
, , , , . . .
() , , . () " ", ().
, f (11, 13, 14, 15) = 1, f = x1x2x3 v x1x2x4 v x1x3x4. x1x2, f = x1x2 (x3 v x4) v x1x3x4, , .
. .
:
1) , 1, (), 0, , 1 - .
|
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2) .
:
1) , 0, (), 1, , 0 - .
2) .
, f (1,3,5,6,7)=1. .
| f = 1 2x3 v 1x2x3 v x1 2x3 v x1x2 3 v x1x2x3; f = (x1 v x2 v x3) (x1 v 2 v x3) ( 1 v x2 v x3). |
:
f = x1x2 v x3;
f = (x1 v x3) (x2 v x3).
0 1, , , .. , 0 (1), 1 (0) .
- .
, .
, f = x1x2 v x3, = ( 1 v 2) 3; .
f = (x1 v x3) (x2 v x3), = 1 3 v 2 3; .
.
, ( ). , .
.
.
Y=f (x1, x2, x3); f (0,2,3,4,5,7)=1.
.
Y.
x1 x2 x3 | f (x1, x2, x3) |
0 0 0 | |
0 0 1 | |
0 1 0 | |
0 1 1 | |
1 0 0 | |
1 0 1 | |
1 1 0 | |
1 1 1 |
:
Y= 1 2 3 v 1x2 3 v 1x2x3 v x1 2 3 v x1 2x3 v x1x2x3
: Fx v F = F
:
Y= 1x2 v x2x3 v x1x3 v x1 2 v 2 3 v 1 3
, , .. . , :
Y1= 1x2 v x1x3 v 2x3;
Y2= 1x2 v x2x3 v x1 2 v 1 3;
Y3= 1x2 v x1x3 v x1 2 v 1 3;
Y4= 1 3 v x2x3 v x1 2;
Y5= 1 3 v 1x2 v x1x3 v x1 2.
, Y1 y4 , .
, . . , , , .
A | |
(0) , .. , (1). (1), , . . , , .
|
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Ȕ - (), 1, 1 1.
. , ( 0). (1) , , ( 1).
A | B | C |
1 2 ( 0), , , R .
(1). , , . , , .
(1) .
, Ȼ, Ȼ, Ż - , . , , , , , , (. ), .
, , , .. : .
. (1 ).
, Ȕ .
Ŕ , .. :
.
,
: :
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- Y = Ē /\ I \/ Ē /\ A \/ Ā /\ E
.
1. .
2) .
, , , . .
|
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:
1) f (1,2,3,4) = 1; f (2,4,5,6,7) = 1; f (1,2,3,8,13,14,15) = 1;
2) f (1,2,4,5) = 1; f (3,4,5,6,7) = 1; f (1,2,4,8,12,14,15) = 1;
3) f (1,2,5,6) = 1; f (1,3,5,6,7) = 1; f (1,2,5,7,13,14,15) = 1;
4) f (1,2,6,7) = 1; f (1,3,4,6,7) = 1; f (1,2,4,9,11,12,15) = 1;
5) f (0,2,4,6) = 1; f (1,2,4,5,7) = 1; f (0,3,5,10,12,13,14) = 1;
6) f (0,3,5,6) = 1; f (0,1,2,6,7) = 1; f (1,2,3,5,7,10,14) = 1;
7) f (1,2,5,7) = 1; f (0,3,4,5,7) = 1; f (1,2,4,5,8,12,13) = 1;
8) f (0,4,5,7) = 1; f (1,2,3,6,7) = 1; f (4,5,6,8,9,11,12) = 1;
9) f (0,1,2,3) = 1; f (3,4,5,6,7) = 1; f (8,9,11,12,13,14,15) = 1;
10) f (2,3,4,5) = 1; f (0,1,3,6,7) = 1; f (7,10,11,12,13,14,15) = 1;
11) f (3,4,5,6) = 1; f (0,1,2,5,7) = 1; f (0,4,8,12,13,14,15) = 1;
12) f (1,2,3,5) = 1; f (0,3,4,6,7) = 1; f (2,4,7,8,9,12,15) = 1;
13) f (1,2,3,6) = 1; f (0,2,4,5,7) = 1; f (3,6,9,12,13,14,15) = 1;
14) f (1,2,3,7) = 1; f (0,1,4,6,7) = 1; f (2,4,6,8,11,13,15) = 1;
15) f (1,2,4,6) = 1; f (0,1,4,5,7) = 1; f (0,5,7,10,11,12,13) = 1;
16) f (1,2,4,7) = 1; f (0,2,4,6,7) = 1; f (1,6,9,10,11,12,14) = 1;
17) f (0,1,3,6) = 1; f (1,2,4,5,6) = 1; f (0,2,4,9,11,12,13) = 1;
18) f (0,1,4,5) = 1; f (1,2,3,4,6) = 1; f (0,1,4,5,8,9,12) = 1;
19) f (0,1,3,5) = 1; f (1,2,4,6,7) = 1; f (1,2,4,15,9,10,12) = 1;
20) f (1,3,5,6,7) = 1; f (0,1,2,3,4) = 1; f (6,7,9,11,12,13,15) = 1;
21) f (1,2, 4, 5,6) = 1; f (1,3,5,6,7) = 1; f (1,2,5,7, 11,13,14,15) = 1;
22) f (1,2,5,6,7) = 1; f (1,3,4,6,7) = 1; f (1,2,4,7, 9,11,12,15) = 1;
23) f (1,2, 3,5,6) = 1; f (0,1,3,5,6,7) = 1; f (1,2,5,7,13,14,15) = 1;
24) f (1,2,6,7) = 1; f (1,3,4,6,7, 9) = 1; f (1,2,4, 5, 9,11,12,15) = 1;
25) f (1,2,5,6) = 1; f (0, 1,6,7) = 1; f (1,2,5,6,7,13,14,15) = 1;
26) f (1,2,6,7) = 1; f (1,3,4,6,7) = 1; f (1,2,4,9, 10,11,12,15) = 1;
27) f (0,1,2,5,6) = 1; f (1,3,5,6,7) = 1; f (1,2,5,7,13,14,15) = 1;
28) f (0,1,2) = 1; f (1,3,4,6,7) = 1; f (1,2,4,9,11,12,13) = 1;
29) f (1,2,5,6) = 1; f (1,3,5,6,7) = 1; f (1,2,5,7,13,14,15) = 1;
30) f (1,2,3,7) = 1; f (1,3,4,6,7) = 1; f (1,2,4,5,8,9,11,) = 1;