Question

Упростите следующие формулы (см. вложение)

Answer 1

$1. overline{(x+y)(xoverline z)}=overline{xxoverline z+xyoverline z}=overline{xoverline z+xyoverline z}=overline{xoverline z(1+y)}= \ overline{xoverline z}=overline x+z \ 2. xy+overline xy+xoverline y=y(x+overline x)+xoverline y=y+xoverline y=x+y \ 3. x(xto y)(xtooverline y)=x(overline x+y)(overline x+overline y)=xy(overline x+overline y)=0$
$4. (xto(yto z))(zto(xto y))(yto(zto x))= \ (overline x+(overline y+z))(overline z+(overline x+y))(overline y+(overline z+x))= \ (overline x+overline y+z)(overline x+y+overline z)(x+overline y+overline z)= \ (overline x+overline xy+overline x , overline z+overline x , overline y+overline y ,overline z+overline xz+yz)(x+overline y+overline z)= \ (overline x(1+y+overline z+overline y+z)+yz+overline y,overline z)(x+overline y+overline z)=$
$(overline x+yz+overline y,overline z)(x+overline y+overline z)= overline x,overline y+overline x,overline z+xyz+xoverline y,overline z+overline y,overline z+overline y,overline z= \ overline x,overline y+overline x,overline z+xyz+overline y,overline z(x+1)=overline x,overline y+overline x,overline z+xyz+overline y,overline z$