2. Construct a truth table for the following:

a) xyz + x(yz) + x(y + z) + (xyz)

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

6. Using DeMorgans Law, write an expression for the complement of F if F (x, y, z) = xz(xy + xz) + xy(wz + y).

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))

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.

40. Construct the XOR operator using only AND, OR, and NOT gates.

51. How many inputs does a decoder have if it has 64 outputs?