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 + Y\')\' Z + (XZ)\' + Y? Partial credit is granted for incomplete simplifications. XY\'Z + XZ\' + Y X + Y X\' + Y + Z\' X\'YZ + X\' + Y + Z\' XY\' + Z\' + Y

Solution

The function is F(x,y,z) = (x+y\')\' z + (xz)\' +y

Formula : (A+B)\' = A\' B\'.

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

Apply double negation law : (A\')\' = A.

= x\' y z + x\' + z\' + y

Therefore F(x,y,z) = x\' y z + x\' + y + z\'

Option 4 is correct choice.