1. Laws (Theorems) of Boolean algebra Laws of Complementation oThe term complement means, to invert or to change 1's to 0's and 0's to 1's, for which purpose inverters or NOT gates are used. oA complement of a variable is represented by a bar over the letter. For example, the complement of a variable A will be denoted by

2. Law 1: = 1 Law 2: = 0 Law 3: If A = 0, Law 4: If A = 1, Law 5:

3. AND Laws Law 6: A.0=0 Law 7: A.1=A Law 8: A.A=A Law 9:

4. OR Laws Law 10: A +0 = A Law 11: A +1 = 1 Law 12: A +A = A Law 13:

5. Commutative Laws –This states that the order in which the variables are OR’ed and AND’ed will make no difference in the output. Law14: A. B = B. A Law 15 : A + B = B + A

6. Associative Laws  This law states that the order in which the variables are grouped will not make any difference in the output. Law 16: A + (B + C) = (A + B) + C

7. Law 17: A.(B.C) = (A.B).C

8. Distributive Laws These laws allow the factoring or multiplying out of expressions. Law 18: A.(B +C) = (A.B) + (A.C) Law 19: A + (B.C) = (A + B) (A + C)

9. De Morgan's Theorems 1. 2. The complement of any Boolean expression is found by using these two rules.

10. Steps for complementation: 1. Replace ‘+’ symbols with ‘.’ symbols and ‘.’ symbols with ‘+’ symbols. 2. Complement each term.

11. Proof of De Morgan's Theorems