1. a. Use DeMorgan's Law to write an expression for the complement of F, if F(x,y,z) = x(y' + z). b. F(x,y,z) = xy + x'z+yz'. F(w,x,y,z) = xyz' (y'z + x)' +(w'yz + x'). c. 2. Simplify the following functional expressions using Boolean algebra and its identities. Name the identity used at each step. a. X'yz + xz b. (x + y)'(x' +y')' c. (x'y"z)' d. xy + xy' e. x'yz + xz f. wx + w(xy + yz') g. xyz + x'yz' + xyz + xyz' h. w'x'y'z' + w'xy'z' + xx'y'z' i. x' (y'z + yz) + xyz 3. Use Boolean Algebra to prove the following either True or False. yz + xyz' + x' y' z=xy + x'z