Question

Simplify F= xy^z + yz + ( x+ y) z^+x^y^​

Answer 1

Answer:

Let

Y = (x+y)(y+z)(x'+z)

According to Distributive law [(p+q)(p+r)=p+qr]

=> Y= (y+xz)(x'+z)

=> Y= y(x'+z)+xz(x'+z)

=> Y= x'y+yz+0+xz [since xz.x’=0]

=> Y= x'y+yz+xz

In order to simplify above, I am making Y into sum of minterms.

According to complement law [A+A'=1]

=> Y= x'y(z+z')+(x+x')yz+x(y+y')z

=> Y= x'yz+x'yz'+xyz+x'yz+xyz+xy'z

Rearrange the terms in Y to simplify

=> Y= x'yz+x'yz+x'yz'+xyz+xyz+xy'z

According to Idempotent law [A+A=A]

=> Y= x'yz+x'yz'+xyz+xy'z

=> Y= x'y(z+z')+xz(y+y')

According to complement law [A+A'=1]

=> Y= x’y+xz