1. Boolean Algebra

2. Laws of Boolean Algebra
Expression
Addition: A + B = B + A
Multiplication: A B = B A
Commutative
Addition: A + (B+C) = (A+B) + C
Multiplication: A(BC) = (AB)C
Associative
Distributive
A(B+C) = AB + AC
(A + B)(C + D) = AC+BC+AD+BD

3. Rules of Boolean Algebra
A + 0 = A
A + 1 = 1
A + A = A
A + A = 1
A · 0 = 0
A · 1 = A
A · A = A
A · A = 0
A = A
A + AB = A
A + AB = A + B
(A + B)(A + C) = A + BC

4. Boolean Algebra
Sample Problems

5. Boolean Simplification
Rule applied
Commutative
A·A = A
A·1 = A

6. Boolean Simplification
Rule applied
Commutative.
A·A = A
A·0 = 0

7. Boolean Simplification
Rule Applied
A · A = A
Commutative
A + A = A
Commutative.
A + AB = A

8. Boolean Simplification
Rule Applied
A + 0 = A

9. Boolean Simplification
Rule Applied
A · A = A
A + 1 = 1

10. Boolean Simplification
Rule Applied
A + AB = A
A + AB= A + B
Associative.
A + A = A

11. Boolean Simplification
Rule Applied
A + AB = A + B
Commutative.
A + AB = A

12. Boolean Simplification
Rule Applied
A + A = A
Distributive.
A + A = 1
A · 1 = A