The document outlines the laws of Boolean algebra and provides examples of simplifying Boolean expressions using these laws. It lists 10 laws of Boolean algebra, including identity, complement, idempotent, dominant, involution, commutative, associative, distributive, DeMorgan's, and absorption laws. It then gives 3 examples of simplifying Boolean expressions such as (A+B)(A+C), AB'C(C+BD)+A'B', and A'BC + AB'C' + A'B'C' + AB'C + ABC by applying the distributive, complement, and other laws.

4. OUTLINE:
 LAWS OF BOOLEAN ALGEBRA
 SIMPLIFICATION OF BOOLEAN
EXPRESSIONS USING BOOLEAN
LAWS

5. LAWS OF BOOLEAN ALGEBRA:
1. IDENTITY LAW:
LAW OF ADDITION
X + 0 = X
LAW OF MULTIPLICATION
X · 1 = X

6. LAWS OF BOOLEAN ALGEBRA:
2. COMPLEMENT LAW:
LAW OF ADDITION
X + X´ = 1
LAW OF MULTIPLICATION
X · X´ = 0

7. LAWS OF BOOLEAN ALGEBRA:
3. IDEMPOTENT LAW:
LAW OF ADDITION
X + X = X
LAW OF MULTIPLICATION
X · X = X

8. LAWS OF BOOLEAN ALGEBRA:
4. DOMINANT LAW:
LAW OF ADDITION
X + 1 = 1
LAW OF MULTIPLICATION
X · 0 = 0

9. LAWS OF BOOLEAN ALGEBRA:
5. INVOLUTION LAW:
(X´)´ = X

10. LAWS OF BOOLEAN ALGEBRA:
6. COMMUTATIVE LAW:
LAW OF ADDITION
X + Y = Y + X
LAW OF MULTIPLICATION
X · Y = Y · X

11. LAWS OF BOOLEAN ALGEBRA:
7. ASSOCIATIVE LAW:
LAW OF ADDITION
X+(Y+Z)=(X+Y)+Z
LAW OF MULTIPLICATION
X·(Y·Z)=(X·Y)·Z

12. LAWS OF BOOLEAN ALGEBRA:
8. DISTRIBUTIVE LAW:
LAW OF ADDITION
X·(Y+Z)=X·Y+X·Z
LAW OF MULTIPLICATION
X+Y·Z=(X+Y)·(X+Z)

13. LAWS OF BOOLEAN ALGEBRA:
9. DEMORGAN’S LAW:
LAW OF ADDITION
(X+Y)´= X´ · Y´
LAW OF MULTIPLICATION
(X·Y)´= X´ + Y´

14. LAWS OF BOOLEAN ALGEBRA:
10. ABSORPTION LAW:
LAW OF ADDITION
X+(X·Y) = X
LAW OF MULTIPLICATION
X·(X+Y) = X

15. SIMPLIFICATION OF SOME BOOLEAN EXPRESSIONS
USING BOOLEAN LAWS:
1. (A+B)(A+C)
SOL: BY DISTRIBUTIVE LAW
AA+AC+AB+BC
BY IDEMPOTENT LAW
A+AC+AB+BC
TAKING A COMMON
A(1+C)+AB+BC
BY DOMINANT LAW
A(1)+AB+BC
BY IDENTITY LAW
A+AB+BC
TAKING A COMMON
A(1+B)+BC
BY DOMINANT LAW
A(1)+BC
BY IDENTITY LAW
A+BC

16. SIMPLIFICATION OF SOME BOOLEAN EXPRESSIONS
USING BOOLEAN LAWS:
2. [AB´(C+BD)+A´B´ ]C
SOL: BY DISTRIBUTIVE LAW
[AB´C+AB´BD+A´B´]C
BY COMPLEMENT LAW
[AB´C + A·0·D + A´B´]C
BY DOMINANT LAW
[AB´C + A´B´]C
BY DISTRIBUTIVE LAW
AB´CC + A´B´C
BY IDEMPOTENT LAW
AB´C + A´B´C
TAKING A COMMON
B´C(A+A´)
BY COMPLEMENT LAW
BC (1)
BY IDENTITY LAW
BC

17. SIMPLIFICATION OF SOME BOOLEAN EXPRESSIONS
USING BOOLEAN LAWS:
3. A´BC + AB´C´ + A´B´C´ + AB´C + ABC
SOL: TAKING BC COMMON
BC(A´+A) + AB´C´ + A´B´C´ + AB´C
BY COMPLEMENT LAW
BC (1) + AB´C´ + A ´B´C´ + AB´C
BY IDENTITY LAW
BC + AB´C´ + A´B´C´ + AB´C
TAKING AB´ COMMON
BC + AB´(C´ + C) + A´B´C´
BY COMPLEMENT LAW
BC + AB´ (1) + A´B´C´
BY IDENTITY LAW
BC + AB´ + A´B´C´
TAKING B´ COMMON
BC + B´(A+A´C´)
BY DISTRIBUTIVE & COMPLEMENT LAW
BC + B´(A+C´)
BY DISTRIBUTIVE LAW
BC + B´A+B´C´