# 09 - Complement and Absorptive laws

1. A variable AND’ed with its complement is always equal to _____

2. A variable OR’ed with its complement is always equal to _____

3. The absorptive law enables a reduction in a complicated expression to a simpler one by absorbing like terms.

FALSE

TRUE

4. A + (A.B) = ____ (OR Absorption Law)

AB

B

A

A+B

5. _________ = A (AND Absorption Law)

AB(AB)

A+B(B+A)

A(A + B)

AA(BB)

6. A+(A+ B) could be reduced to:

B

(A+B)

A

AB

7. A+(A* B) could be reduced to:

B

(A+B)

AB

A

8. A*(A+B) could be reduced to:

AB

(A+B)

B

A

9. A*(A+B)*A*(A+B)+B could be reduced to:

A

(A+B)

AB

B

10. A*(A+B)*A*(A+B)*A*(A+B) could be reduced to:

B

A

(A+B)

AB

11. A+(A*B)*A*(A+B) could be reduced to:

AB

B

(A+B)

A

12. B+(A*B)*B+(A+B) could be reduced to:

B

AB

A

(A+B)

13. B+(A*B) could be reduced to:

A

(A+B)

AB

B

14. B*(B+A) could be reduced to:

B

AB

(A+B)

A

15. B*(B+A)*B*(C+B) could be reduced to:

(A+B)

A

AB

B

16. A * ~A = 0 (complement law)

FALSE

TRUE

17. A + ~A = 1 (complement law)

TRUE

FALSE

18. ~(A * B) * (~A + B) * (~B + B) could be reduced to ~(A * B) * (~A + B) * 1 using the _________ law.

absorptive

commutation

complement

double negation

19. Using the complement law, ~A + ~B * B could be reduced to _____________

1

~A + 0

A

A1

20. Both of the below equations can be simplified, using __________ to A.

absorption

distribution

complementation

commutation

21. (A * B) + (A * ~B) = A

FALSE

TRUE

22. (A + B) * (A + ~B) = B

TRUE

FALSE

23. (A + B) * (A + ~B) =A

FALSE

TRUE

24. A + (~A * B) = A + B

FALSE

TRUE

25. A * (~A + B) =

A *B

A

A+B

B