Boolean Algebra Quiz

1. Give the relationship that represents the dual of the Boolean property A + 1 = 1?
   (Note: * = AND, + = OR and ' = NOT)
   1. A * 1 = 1
   2. A * 0 = 0
   3. A + 0 = 0
   4. A * A = A
   5. A * 1 = 1
   
   
2. Give the best definition of a literal?
   1. A Boolean variable
   2. The complement of a Boolean variable
   3. 1 or 2
   4. A Boolean variable interpreted literally
   5. The actual understanding of a Boolean variable
   
   
3. Simplify the Boolean expression (A+B+C)(D+E)' + (A+B+C)(D+E) and choose the best answer.
   1. A + B + C
   2. D + E
   3. A'B'C'
   4. D'E'
   5. None of the above
   
   
4. Which of the following relationships represents the dual of the Boolean property x + x'y = x + y?
   1. x'(x + y') = x'y'
   2. x(x'y) = xy
   3. x*x' + y = xy
   4. x'(xy') = x'y'
   5. x(x' + y) = xy
   
   
5. Given the function F(X,Y,Z) = XZ + Z(X'+ XY), the equivalent most simplified Boolean representation for F is:
   1. Z + YZ
   2. Z + XYZ
   3. XZ
   4. X + YZ
   5. None of the above
   
   
6. Which of the following Boolean functions is algebraically complete?
   1. F = xy
   2. F = x + y
   3. F = x'
   4. F = xy + yz
   5. F = x + y'
   
   
7. Simplification of the Boolean expression (A + B)'(C + D + E)' + (A + B)' yields which of the following results?
   1. A + B
   2. A'B'
   3. C + D + E
   4. C'D'E'
   5. A'B'C'D'E'
   
   
8. Given that F = A'B'+ C'+ D'+ E', which of the following represent the only correct expression for F'?
   1. F'= A+B+C+D+E
   2. F'= ABCDE
   3. F'= AB(C+D+E)
   4. F'= AB+C'+D'+E'
   5. F'= (A+B)CDE
   
   
9. An equivalent representation for the Boolean expression A' + 1 is
   1. A
   2. A'
   3. 1
   4. 0
   
   
10. Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?
    1. ABCDEF
    2. AB
    3. AB + CD + EF
    4. A + B + C + D + E + F
    5. A + B(C+D(E+F))