Информ. - тема ЛогикаУпростить следующие выражения:
1. (X v Z v Y) & (X v ¬Y v Z) & (X v ¬Y v ¬Z)
2. (A v ¬B) v A v F & E v B
3. X v T & Y & Z & ¬(X v T)
1)
(X+Z+Y)(X+!Y+Z)(X+!Y+!Z) -> X(X+!Y+Z)(X+!Y+!Z)+Z(X+!Y+Z)(X+!Y+!Z)+Y(X+!Y+Z)(X+!Y+!Z) X(X+!Y+Z)(X+!Y+!Z) -> XX(X+!Y+!Z)+!YX(X+!Y+!Z)+ZX(X+!Y+!Z) XX(X+!Y+!Z) -> XX+!YX+!ZX XX -> X XX+!YX+!ZX -> X !YX(X+!Y+!Z) -> X!YX+!Y!YX+!Z!YX X!YX -> X!Y !Y!YX -> !YX X!YX+!Y!YX+!Z!YX -> X!Y ZX(X+!Y+!Z) -> XZX+!YZX+!ZZX XZX -> XZ !ZZX -> 0 XZX+!YZX+!ZZX -> XZ XX(X+!Y+!Z)+!YX(X+!Y+!Z)+ZX(X+!Y+!Z) -> X Z(X+!Y+Z)(X+!Y+!Z) -> XZ(X+!Y+!Z)+!YZ(X+!Y+!Z)+ZZ(X+!Y+!Z) XZ(X+!Y+!Z) -> XXZ+!YXZ+!ZXZ XXZ -> XZ !ZXZ -> 0 XXZ+!YXZ+!ZXZ -> XZ !YZ(X+!Y+!Z) -> X!YZ+!Y!YZ+!Z!YZ !Y!YZ -> !YZ !Z!YZ -> 0 X!YZ+!Y!YZ+!Z!YZ -> !YZ ZZ(X+!Y+!Z) -> XZ+!YZ+!ZZ !ZZ -> 0 XZ+!YZ+!ZZ -> XZ+!YZ XZ(X+!Y+!Z)+!YZ(X+!Y+!Z)+ZZ(X+!Y+!Z) -> XZ+!YZ Y(X+!Y+Z)(X+!Y+!Z) -> XY(X+!Y+!Z)+!YY(X+!Y+!Z)+ZY(X+!Y+!Z) XY(X+!Y+!Z) -> XXY+!YXY+!ZXY XXY -> XY !YXY -> 0 XXY+!YXY+!ZXY -> XY !YY(X+!Y+!Z) -> 0 ZY(X+!Y+!Z) -> XZY+!YZY+!ZZY !YZY -> 0 !ZZY -> 0 XZY+!YZY+!ZZY -> XZY XY(X+!Y+!Z)+!YY(X+!Y+!Z)+ZY(X+!Y+!Z) -> XYX(X+!Y+Z)(X+!Y+!Z)+Z(X+!Y+Z)(X+!Y+!Z)+Y(X+!Y+Z)(X+!Y+!Z) -> X+!YZ
2)
(A+!B)+A+FE+B -> 1
3)
!(X+T) -> !X!T TYZ(!(X+T)) -> 0X+TYZ(!(X+T)) -> X
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Answers & Comments
1)
(X+Z+Y)(X+!Y+Z)(X+!Y+!Z) -> X(X+!Y+Z)(X+!Y+!Z)+Z(X+!Y+Z)(X+!Y+!Z)+Y(X+!Y+Z)(X+!Y+!Z)
X(X+!Y+Z)(X+!Y+!Z) -> XX(X+!Y+!Z)+!YX(X+!Y+!Z)+ZX(X+!Y+!Z)
XX(X+!Y+!Z) -> XX+!YX+!ZX
XX -> X
XX+!YX+!ZX -> X
!YX(X+!Y+!Z) -> X!YX+!Y!YX+!Z!YX
X!YX -> X!Y
!Y!YX -> !YX
X!YX+!Y!YX+!Z!YX -> X!Y
ZX(X+!Y+!Z) -> XZX+!YZX+!ZZX
XZX -> XZ
!ZZX -> 0
XZX+!YZX+!ZZX -> XZ
XX(X+!Y+!Z)+!YX(X+!Y+!Z)+ZX(X+!Y+!Z) -> X
Z(X+!Y+Z)(X+!Y+!Z) -> XZ(X+!Y+!Z)+!YZ(X+!Y+!Z)+ZZ(X+!Y+!Z)
XZ(X+!Y+!Z) -> XXZ+!YXZ+!ZXZ
XXZ -> XZ
!ZXZ -> 0
XXZ+!YXZ+!ZXZ -> XZ
!YZ(X+!Y+!Z) -> X!YZ+!Y!YZ+!Z!YZ
!Y!YZ -> !YZ
!Z!YZ -> 0
X!YZ+!Y!YZ+!Z!YZ -> !YZ
ZZ(X+!Y+!Z) -> XZ+!YZ+!ZZ
!ZZ -> 0
XZ+!YZ+!ZZ -> XZ+!YZ
XZ(X+!Y+!Z)+!YZ(X+!Y+!Z)+ZZ(X+!Y+!Z) -> XZ+!YZ
Y(X+!Y+Z)(X+!Y+!Z) -> XY(X+!Y+!Z)+!YY(X+!Y+!Z)+ZY(X+!Y+!Z)
XY(X+!Y+!Z) -> XXY+!YXY+!ZXY
XXY -> XY
!YXY -> 0
XXY+!YXY+!ZXY -> XY
!YY(X+!Y+!Z) -> 0
ZY(X+!Y+!Z) -> XZY+!YZY+!ZZY
!YZY -> 0
!ZZY -> 0
XZY+!YZY+!ZZY -> XZY
XY(X+!Y+!Z)+!YY(X+!Y+!Z)+ZY(X+!Y+!Z) -> XY
X(X+!Y+Z)(X+!Y+!Z)+Z(X+!Y+Z)(X+!Y+!Z)+Y(X+!Y+Z)(X+!Y+!Z) -> X+!YZ
2)
(A+!B)+A+FE+B -> 1
3)
!(X+T) -> !X!T
TYZ(!(X+T)) -> 0
X+TYZ(!(X+T)) -> X