Why is in Boolean Algebra
(x+y*z)*(x+y*z) = x?
I don't understand how
x(y(z*~z)) = x instead of xy
Expand the following:
(x+y z) (x+y z)=x
(x+y z) (x+y z)=(x+y z)^2:
(x+y z)^2=x
(y z+x) (y z+x)=(y z) (y z) + (y z) (x) + (x) (y z) + (x) (x)=y^2 z^2+x y z+x y z+x^2=x^2+2 x y z+y^2 z^2:
x^2+2 x y z+y^2 z^2=x
Subtract x from both sides of x^2+2 x y z+y^2 z^2=x:
x^2+2 x y z+y^2 z^2-x=x-x
x-x=0:
Answer: | x^2 + 2xyz + y^2 z^2 - x=0
