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xÚ(yÚz) = (xÚy)Úz | xÙ(yÙz) = (xÙy)Ùz | (4) | |
xÙ(yÚz) = xÙyÚ xÙz | xÚ yÙz = (xÚy) Ù (xÚz) | (5) | |
(xÚy)= xÙ(y) | (xÙy)= xÚ(y) | (6) | |
xÚx=x | xÙx=x | (7) | |
xÚxÙy=x | xÙ(xÚy)=x | (8) | |
xÙyÚ(x)Ùy=y | (xÚy)Ù (xÚy)=y | (9) | |
xÚ(x)=1 | xÙ(x)=0 | (10) | |
xÚ1=x; xÚ0= | xÙ1=x; xÙ0=0 | (11) | |
(x)=x | (12) |
1. ( 11 2004 .)
:
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1) | 2) | 3) | 4) |
.
:
= | (13) |
= | (14) |
: (A → B). , (1), (6), (12):
(1) | (6) | (12) |
(A → B) = ((A) Ú B) = (A) Ù (B) = A Ù (B)
(13), (14), , :
Ù ( ),
Ù .
( 3).
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2. ( 12 2004 .)
(A Ú B)
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, (6), (12):
(6) (12)
(A Ú B) = A Ù (B) = A Ù B, 4.
: 4
3. ( 13 2004., 11 2005, 2006.)
F : X, Y, Z. F:
X | Y | Z | F |
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1. F . F , 0, X=0, Y=0, Z=1, XÚYÚZ. , F.
2. :
1) F=XÙYÙZ=0 X=0, Y=0, Z=0, .
2) F=XÚYÚZ=1 X=0, Y=0, Z=1, .
3) XÚYÚZ F X,Y,Z.
4) F=XÚYÚZ=1 X=0, Y=0, Z=1, .
, 3.
: 3
4. ( 9 2005 ., 2006 .)
X
X>1 Ù ((X<5)→(X<3)) | (15) |
1) 1 | 2) 2 | 3) 3 | 4) 4 |
.
, , (1):
(1)
(X>5)→(X<3) = (X<5) Ú (X<3)
(15):
(X>1)Ù((X<5)→(X<3)) = (X>1) Ù((X<5) Ú (X<3)) = =(X>1) Ù ((X>=5) Ú (X<3)) | (16) |
(16) X (=1; 2; 3; 4)
X=1: (1>1) Ù((1>=5) Ú (1<3)) = 0Ù(1Ú1) = 0Ù1=0
X=2: (2>1) Ù((2>=5) Ú (2<3)) = 1Ù(0Ú1) = 1Ù1=1
X=3: (3>1) Ù((3>=5) Ú (3<3)) = 1Ù(0Ú0) = 1Ù0=0
X=4: (4>1) Ù((4>=5) Ú (4<3)) = 1Ù(0Ú0) = 1Ù0=0
2.
: 2.
5. ( 10 2005 ., 2006 .)
, (AÙB)
1) A Ú B | 2) A Ú B | 3) B ÙA | 4) A ÙB |
.
(6) (12):
(6) (12)
(AÙB) = (A)ÚB = AÚB
1.
: 1.
6. ( 13 2005 ., 2006 .)
5 ( , ). :
A | B | C | D | E |
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7. ( 14 2005 ., 2006 .)
, : A, B, C, D, E. , , . , , , . , D, E, . ?
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8. ( 2 2005 ., 2006 .)
(KÙLÙM) Ú (LÙMÙN)=1
K, L, M, N ?
K, L, M N, . .
.
, , () , :
KÙLÙM=1 | (17) |
LÙMÙN=1 | (18) |
(17) , , 1, , , .. =L=M=1. N , : 1) =L=M=1, N=1; 2) =L=M=1, N=0.
(18) , , 1, , L=M=N=1. : L=M=0, N=1. K , (18) : 1) =M=0, N=1, K=1; 2)=M=0, N=1,k=0.
, (17) 2 (18) . , (17) (18), .. 4.
: 4.
9. ( 2 2004 .)
K, L, M, N,
(KÚ M) → (LÚ MÚ N)
. : K, L, M N ( ). , , 1101 , K=1, L=1, M=0, N=1.
.
, (1), (6), (12):
(1) (6), (12)
(KÚ M) → (LÚ MÚ N) = (KÚ M) Ú (LÚ MÚ N) = (K Ù M) Ú (LÚ MÚ N) = 0
(K Ù M) (LÚ MÚ N), ,
K Ù M =0 | (19) |
LÚ MÚ N =0 | (20) |
(20) , L= M= N =0, L=1, M=0, N=0.
M=0 (19):
K Ù 1 =0, K=0.
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: K=0, L=1, M=0, N=0.
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10. ( 4 2006 .)
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E=0 Ù F=0 Ù A=1 Ù B=1 Ù C=1 Ù D=1.
: A= C E=B, :
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11. ( 8 2006 .)
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1. | - . / .., .., .., ..; . .. . -, 2005 136 . |
2. | . 10-11 / .. .. .: . , 2003. 512 .: . |
3. | . / .. .., . . , .. . .: . , 2002. 400 .: . |
4. | : . 10-11 . / . . . 3- . .: , 2003. 416 .: . |
5. | : 6 2005.- .: , 2005. 104 .: . |
6. | . 2004 . |
7. | . 2005 . |
8. | . 2006 . |
9. | 4 . .. / , 2005 . |
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1. :
Ù ( → ):
1) | 2) | 3) | 4) |
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3. (X Ú Y) Ù X?
4. F(A,B) :
A | B | F |
5. 4 , , . . , , , . ? (: , , , )
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(Z<X Ú Z<Y) Ù (Z+1< X) Ù (Z+1< Y)
Z, X=20, Y=10?
7. . , . , , , , , , . , , , . ?
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Ȕ |, Ȕ - &.
A | & |
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& & & | |
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xÚy | xÙy | A→B =AÚB | Z=19 |