I need help on following question Please simplified The Bool

I need help on following question.

Please simplified The Boolean function F(x, y, z) = xy\'z + (x + z\' + xz\')\' to simplest form using boolean identity.

Solution

F = xy\'z + (x + z\' + xz\')\'

= xy\'z +(x\'.(z\')\'.(xz\')\') since (a+b)\'=a\'b\'

= xy\'z + (x\'.z.(x\' + (z\')\')) since (ab)\'=a\'+b\'

=xy\'z + x\'x\'z + x\'.z.z

= xy\'z +x\'z + x\'z since a.a=a

= xy\'z + x\'z since a+a=a

= (xy\'+x\').z