Информ. - тема Логика
Упростить 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