16. Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step.

a) z (w + x) + wxz + wxyz + wxyz

b) y(xz + xz) + z (x + y)

c) x(yz + x)(y + z)

26. Given the Boolean function, F(x, y, z) = xy + xyz

a) Derive an algebraic expression for the complement of F. Express in sum-of-products form.

b) Show that FF. = 0.

c) Show that F + F = 1.

27. Given the function, F (x, y, z) = y(xz + xz) + x(yz + yz)

a) List the truth table for F.

b) Draw the logic diagram using the original Boolean expression.

c) Simplify the expression using Boolean algebra and identities.

d) List the truth table for your answer in Part c.

e) Draw the logic diagram for the simplified expression in Part c.