1. Construct a truth table for the following:

a. xyz + (xyz)'

b. x (yz' + x'y)

2. Using DeMorgan's Law, write an expression for the complement of F if F(x,y,z) = x(y' + z).

3. Is the following distributive law valid or invalid? Prove your answer.

x XOR (y AND z) = (x XOR y) AND (x XOR z)

4. Simplify the following functional expressions using Boolean algebra and its identities. List

the identity used at each step.

a. F(x,y,z) = x'y + xyz' + xyz

b. F(w,x,y,z) = (xy' + w'z)(wx' + yz')

c. F(x,y,z) = (x + y)'(x' + y')'

5. Simplify the following functional expressions using Boolean algebra and its identities. List

the identity used at each step.

a. (ab + c + df)ef

b. x + xy

c. (xy' + x'z)(wx' + yz')

6. Given the Boolean function: F(x,y,z)=x' y + 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.

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