CS 251 Boolean Algebra Homework

In this writeup, A' means "not A" (i.e., A with a bar over it).

1. Simplify A+AB using identities and laws presented in class and in the book. (You may not use the "covering" theorem, of course.) Hint: Begin by factoring the A out of this expression as if it were a "regular" numeric expression.
2. Explain why the result from the previous exercise makes sense intuitively.
3. Simplify A(A+B).
4. Use a truth table to simplify A + A'B.
5. Explain why the result from the previous exercise makes sense intuitively.
6. Use your result from problem 4 to simplify XY + (XY)'B.
7. Simplify A' + AB. Clearly explain how your answer from Problem 4 applies to this problem.
8. Simplify each of the statements below using boolean laws and identities. Show your work.
   1. (A + B)(A + C)(A' + B')
   2. F(E + F + G)
   3. AB + A'B + AB' + A'B'
   4. (A + B)(A' + B')
   5. (B + C' + A'B)(BC + AB' + AC)
   6. AB + AB'
   7. A'BC + AC
   8. AB + A'B + BC
   9. (AB + A'C + BC')'
   10. (A+B+C)'D+AD+B

Additional practice (not due for credit):

1. A' + A(A + B)(B + C')
2. (AB + C)(B + CD)
3. (AB" + A'C)(DA' + BC')
4. A(A'+B)
5. (B + C' + BC')(BC' + AB + AC)
6. (AB' + D'C)(DA' + BC')
7. (AB' + A'B)(DA' + BC')