12. Show that xz = (x + y)(x + y)(x + z)

a) Using truth tables

b) Using Boolean identities

14. 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

c) F (x, y, z) = (x + y + z ) + xyz + yz + xyz

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)