Which is the minimum SOP expression for the function fx y z

Which is the minimum SOP expression for the function f(x, y, z) = x\'yz + xyz + xyz\'? Partial credit is granted for incomplete simplifications. (x\'z + x)y xyz + y x\'yz + xy y xy + yz

Solution

Law to be used to solve the given equation are as follows:

Complementary law:

     X + X’ = 1

     X.X’ = 0

Union Law:

     X + 1 = 1

     X + 0 = X

Intersection Law:

    

     X.1 = X

     X.0 = 0

Simplification of the given equation is as follows:

f(x,y,z) = x’yz + xyz + xyz’

         = x’yz + xy(z+z’)          [z+z’=1]

         = x’yz + xy

         = y(x’z + x)

         = y(x’z + x.1)            [x.1=x]

    = y(x’z + x.(1+z))        [1 + z= 1]

         = y(x’z + x + xz)

         = y(z(x+x’)+ x)           [x+x’=1]

    = y(z + x)

    = xy + yz

Therefore, the correct answer is xy + yz