Answer
a) x + y + z
b) (x + y + z) (x + y + ~z)(x + ~y + z)(~x + y + z)(~x + y + z)
c) (x +y + z)(x + y + ~z)(x + ~y + z)(x + ~y + ~z)
d) (x +y +z)(x + y + ~z) (x + ~y + z) (x + ~y + ~z) (~x + ~y + z) (~x +~y + ~z
Work Step by Step
the product-of-sums expansion of each of the
Boolean functions
a) F(x, y, z) = x + y + z
-- x + y + z
b) (x + y + z) (x + y + ~z)(x + ~y + z)(~x + y + z)(~x + y + z)
-- F(x, y, z) = (x + z)y
c) (x +y + z)(x + y + ~z)(x + ~y + z)(x + ~y + ~z)
-- F(x, y, z) = x
d) F(x, y, z) = x ~y
-- (x +y +z)(x + y + ~z) (x + ~y + z) (x + ~y + ~z) (~x + ~y + z) (~x +~y + ~z)
