demorgans law complement for fwxyz xzxyzx ywz x demorgans la

Solution

f(w,x,y,z)= xz\'(x\'yz+x) +y(w\'z +x\')

using De Morgan\'s laws complement of f

= f\'

= (xz\'(x\'yz+x) +y(w\'z +x\'))\'

=(xz\'(x\'yz+x))\' (y(w\'z +x\'))\'

=((xz\')\'+(x\'yz+x)\') (y\' + (w\'z+x\')\'

= (x\'+z+(x\'yz)\'(x)\') (y\' + (w\'z)\' x)

= (x\'+z+(x+y\'+z\')x\')(y\'+(w+z\')x)

= (x\'+z+xx\'+x\'y\'+x\'z\')(y\'+xw+xz\')

=(x\'(1+x+y\'+z\')+z)(y\'+xw+xz\')

=(x\'+z)(y\'+xw+xz\')

= x\'y\' + zy\' + wxz

= y\'( x\' + z) + wxz