Simplify the following Boolean expressions to a minimum number of literals using only Boolean algebra (show all your steps for credit and show used Theorems and Axioms).

(a) F(a, b, c) = a' b' c' + a c' + a' b' c

(b) F(X, Y ) = (X' + Y ) (X' + Y' )

(c) F(x, y, z) = (x + y + z') (x + y' + z') (x + y + z) (x + y' + z)

(d) F(x, y, z) = x y z' + x' y' z + x' y z + x y' z'