: 230100
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: 230400
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: 220400
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:
2012 .
, ..-.. .. ,
6 " 31 " 2012 .
. ________________..
(, , , , ) ,
___ "___"____________ 20___ .
. ________________..
1 ......................................................... 4
2. ................................ 4
3. ...................................... 13
, (29 ), (28 ).
29 .
, ,
,
.
1.3
7 , 2 , 5 - .
, . [1]., 4.3
. .
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| 1. | (BA); (B(ùAÚC)) |¾ (B(ùBÚC)) |
| (ùAÚB); (CÚùB) |¾ (AC)Ú(AùC) | |
| 3. | (ùAÚùB) |¾ (ù BA)Ú() |
| 4. | (AB) |¾ ((ùBÚC)(ùAÚC)) |
| (AB); (CD) |¾ (A&CB&D) | |
| (AB); (ù AB) |¾ BÚ (AC) | |
| 7. | (BA); (B(AC)) |¾ (BC) |
| 8. | (AB) |¾ (ùCA)(ùCB) |
| (AB); (A(ùBÚC)) |¾ (AC) | |
| 10. | (A&BÚùA&ùB) |¾ (AC)(BC) |
| 11. | (A(BC));(AB);A |¾ C |
| 12. | (A&BC) |¾ (A(BC)) |
| 13. | (B(AC)); (BA) |¾ (B(BC)) |
| (A&BÚC&D); (Aù A) |¾ C | |
| 15. | (A(BC)); (ù DÚA);B |¾ (DC) |
| 16. | (AÚB); (AC); (BD) |¾ CÚD |
| 17. | (AB); (CB); (D(AÚC)); D |¾ B |
| 18. | (AB); (BC); (CD) |¾ (AD) |
| (B(AC)); (BA) |¾ (B(BC)) | |
| (A(CB)); (ù DÚA); C; D |¾ DB | |
| (AB) |¾ (CÚA)(CÚB) | |
| 22. | A; (AB) |¾ (C&AB&C) |
| (AB); ù (BÚC) |¾ ù A | |
| (A(BC)); (ù DÚA);B |¾ (DC) | |
| (AÚC); (AB);A |¾ (AÚC)(BÚC) | |
| (A(BC)); (AB) |¾ (AC) | |
| (ù AÚB); (Cù B) |¾ Aù C | |
| C; (AB) |¾ ((CA)(CB)) | |
| (A(BC)) |¾ ((A&B) C) | |
| (AB) |¾ A&CB&C | |
| 31. | (A(BC)); (ù DÚA);B |¾ (DC) |
| 32. | (AB); (BC); (CD) |¾ (AD) |
| 33. | (B (AC)); (BA) |¾ (BC) |
| 34. | (AB) |¾ (A&C)B&C) |
| 35. | (B(AC)); (BA) |¾ (B(BC)) |
| 36. | (A(BC); (AB) |¾ (A(AC)) |
| 37. | (B(AC)); (BA) |¾ (B(BC) |
| 38. | (AC); (BA) |¾ (ù C&B) |
| 39. | (AB); (CB); (D(AÚC)); D |¾ B |
| 40. | (AB)|¾ (ù AÚù CÚB&C) |
| 41. | (B(AC)); (BA) |¾ (B(BC)) |
| 42. | (A&BC) |¾ (A(BC)) |
| (A(BC)); (ù DÚA);B |¾ (DC) | |
| 44. | (A(BC));(AB);A |¾ C |
| 45. | (A(BC)); (AB) |¾ (AC) |
| 46. | (A(BC)) |¾ (B(AC)) |
| 47. | (AB); (BC); (CD) |¾ (AD) |
| 48. | (AB) |¾ (AÚC)(BÚC) |
| 49. | (AB); B |¾ ù A&ù CÚBÚC |
| 50. | (AB) |¾ (AC)(BC) |
1.1.5
7 , 2 , 5 - .
, . , , . [1] 13.
|
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|
1.1.5
. ( ,
| X | y | z |
, . .
| F(X,Y,Z) | ||||||||
2.1.4 .
11 , 6 , 5 - .
, , , [1], IV, 7.
2.1.4:
. .
| "x(A(x)ù B(y))$y(B(y)ù A(x)) | |
| "x(ù A(x)$x(ù C(x)))"x((C(x)A(x)) | |
| "x(A(x)$x(B(x)))$y(ù A(x)Úù C(y)ÚC(y)&B(x)) | |
| "x(A(x)$x(B(y)))$x(ù A(x)ù B(y)) | |
| "x(A(x)B(y))&"y(A(x)(B(y)C(z))$z(A(x)C(z)) | |
| "x(A(x)$y(B(y)C(z)))"z(A(x)&B(y)C(z)) | |
| "x(A(x)B(z))&"y(C(y)A(x))$z(C(y)B(z)) | |
| "x(A(x)B(y))"y((C(y)ÚA(x))(C(y)Ú$y(B(y))) | |
| "x(A(x)B(y))&"y(A(x)(B(y)C(z)))(A(x)$z(C(z))) | |
| "x(A(x)B(y)&A(x)"y(B(y)C(z)))(A(x)$z(C(z))) | |
| "x(A(x)$z(B(y)C(z)))"y(B(y)(A(x)C(z))) | |
| ("x(A(x))$x(B(x)))"z((B(x)C(z))(A(x)C(z))) | |
| ($x(ù A(x))"x(ù B(x)))(ù B(x)ÚA(x)) | |
| ("x(A(x)))("x(B(x)))$y(C(y)&A(x)C(y)&B(x)) | |
| "(ù ()$(()))(ù ()()) | |
| ("x(B(x))$x(A(x)))&$y((A(x)C(y))(ù C(y)&B(x))) | |
| "x(ù A(x)$y(B(y)))(B(y)ÚA(x)) | |
| "x(ù A(x)$y(ù B(y)))(B(y)A(x)) | |
| "x(A(x)B(x))&$y(B(x)C(y)&$z(C(y)D(z))) | |
| ("x(A(x)B(x))&"z(C(z)A(x)))$y(C(z)B(y)) | |
| ("x(B(x)"y(A(y)))&("y(B(y)(A(x)C(z))))$z(C(z)) | |
| "x(B(x))$y(A(y)B(x)) | |
| "x(A(x)B(x))("y(C(y)A(x))$z(C(z)B(x))) | |
| "x(B(x)A(y))&(B(x)"y(A(y)C(z)))$z(C(z))) | |
| $x(A(x)B(z))$y(C(y)ÚA(x)"z(C(y)ÚB(z))) | |
| ("x(B(x))$x(A(x)))&(A(y)$yC(y))(ù A(x)ÚC(y)) | |
| ("x(A(x))$x(B(x)))$y((A(x)ÚC(y))(B(x)ÚC(y))) | |
| $x(A(x)"y(B(y)))&(ù A(x)"y(B(y)))B(y) | |
| "x(A(x)$y(B(y)))&(ù A(x)B(x))B(x) | |
| "x(ù A(x))(A(x)$y(B(y))) | |
| ($x(B(x))"x(A(x)))&(ù B(x)A(x))A(x) | |
| ("x(B(x))$x(C(x)))(A(y)&B(x)A(y)&C(x)) | |
| $(()())""((()())(()())) | |
| ("x(A(x))$x(C(x)))&"y(C(x)B(y))(A(x)B(y)) | |
| "x(A(x))$y(B(y))&"y(C(y)$xD(x))(A(x)&C(y)) &D(y)) | |
| "x(A(x))(ù A(x)$y(B(y))) | |
| "x(B(x))$y(A(y)B(x)) | |
| "x(B(x)"y(A(y)))&"y(B(y)(A(x)C(z)))$z(B(z) C(z)) | |
| "x(B(x)A(y))&(B(x)"y(A(y)C(z)))$z(B(x)C(z)) | |
| "x(A(x)B(x))"y((C(y)A(x))(C(y)B(x))) | |
| ("x(ù A(x)$y(ù C(y)))(C(x)A(x)) | |
| "x(A(x)ù B(y))$y(B(y)ù A(x)) | |
| $x(A(x)B(z))$y((C(y)ÚA(x))"z(C(y)ÚB(z))) | |
| "x(A(x)B(y))&"z(C(z)A(x))$y(C(z)B(y)) | |
| "(()())&$(()())&$(()())) | |
| "x(ù A(x)$y(ù B(y)))(B(x)A(x)) | |
| "x(ù A(x)$x(B(x)))(B(x)ÚA(x)) | |
| ("x(B(x)$y(A(y))))&$y(A(x)C(y))ù C(y)&B(x) | |
| ("x(ù A(x)$y(B(y))))(ù B(x)A(x)) | |
| "x(A(x)B(y))&"y(A(x)(B(y)C(z)))$z(A(x)C(z)) |
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4.1
9 , 2 , 7 .
, . [1].
4:1
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1. .
2. .
3. .
4. .
5. .
6. .
7. .
8. ( ).
9. ( ).
10. .
11. .
12. , .
13. .
14. , (m = n):
15. , (m = n):
16. 90 .
17. ( ).
18. , ( ).
19. .
20. ( n ).
3.4. .
7 2 , 5 .
, , sdfnm . [1], . 1.
2.5:
1 A ={ a, b, c }. P b (P → bP).
2 A ={ a, b, c }. P bc (P → Pbc).
3 A ={ a, b, c }. a P.
4 A ={ a, b, c }. P (
).
5 A ={ a, b, c }. P (
).
6 A ={ a, b, c }. , P ab. ( ):
ab, , .
7 A ={ a, b, c }. , P a. :
a (, ) ().
8 A ={ a, b, c }. P a, P
b , a.
9 A ={ a, b,0,1}. , P (
, ). : a () ().
10 A ={ a, b,0,1}. , P
( , 0 1). :
1 () 0.
11 A ={0,1}. P ,
, .
12 A ={0,1}. P ,
(1, 2, 4, 8, ) . : 1
() 0.
13 A ={0,1,2,3}. P
, , . : 1
() 0.
14 A ={0,1}. P , -
, P (: 101 → 10100).
15 A ={0,1}. P ,
, P 2
(: 1011 → 101).
16 A ={ a, b, c }. P (0, 2, 4, ), a,
.
17 A ={0,1,2}. P
, , . : 1 () 0.
(: )
18 A ={ a, b, c }. P . P
|
|
|
.
19 A ={ a, b, c }. P ,
.
20 A ={ a, b, c }. P .
21 A ={ a, b }. P ,
. : a () .
22 A ={ a, b }. P
.
23 A ={ a, b }. , P (, -
) . : a () .
24 A ={ a, b }. P a bb.
25 A ={ a, b, c }. P ab c.
26 A ={ a, b }. P (: abb → abbabb).
27 A ={ a, b }. P (: bab → bbaabb).
28 A ={ a, b }. P (: abb → bba).
29 A ={0,1}. P ,
, . (: ,
.)
30 A ={0,1,2,3}. P
, .
31 A ={0,1,2}. P
, __
2
1. , . . : . / . . . 3- . . [ .]: , 2009. 384 .: . ( ). .: . 368-369. . .: . 370-383. ISBN 978-5-91180-759-7 (( .))
2. . M., . . . . - . " . " / . . , . . . .: "", 1999. 288 .
3. , . / .,.,.;. ...; .... .: , 1979. 536. .
4. .., .. . " ". .3, .2006. . 240 . ISBN 5-484-00520-5
