Total points: 50 (10 points for each question) Using De Morgan's Law, write an expression for the complement of F if F(x, y, z) = xy(x + 2). (2) Use any method to prove the following either true or false. x2 + xy + y2 = x2 + y Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step.a) F(x, y, z)=y(x + (x + y)) b)F(x, y, z) = x 'yz + xz Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step. a) z (w + x)' + w'xz+wxyz' + wx'yz' b) y(x+2" + x2)+2(x + y) c) xyz' + x)(y + 2) (5) Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step. a) y(xx' + xz) + y(x2 + x'z) b)x(yz + y) + x(y+zy c) x[y'z + fy +z'/][x'y +z)