Postulates and Theorems of Boolean Algebra :)

 Postulates and Theorems of Boolean Algebra 

Duality Principle:

This property of Boolean algebra state that all binary expressions remain valid when following two steps are performed


Using Boolean algebra techniques, the expression may be significantly simplified:

 Assume A, B, and C are logical states that can have the values 0 (false) and 1 (true)."+" means OR, "·" means AND, and ^NOT[A] means NOT A

 Postulates 

(1)	A + 0 = A	A · 1 = A	identity
(2)	A + NOT[A] = 1	A · NOT[A] = 0	complement
(3)	A + B = B + A	A · B = B · A	commutative law
(4)	A + (B + C) = (A + B) + C	A · (B · C) = (A · B) · C	associative law
(5)	A + (B · C) = (A + B) · (A + C)	A · (B + C) = (A · B) + (A · C)	distributive law

Theorems 

(6)	A + A = A	A · A = A
(7)	A + 1 = 1	A · 0 = 0
(8)	A + (A · B) = A	A · ( A + B) = A
(9)	A + (NOT[A] · B) = A + B	A · (NOT[A] + B) = A · B
(10)	(A · B) + (NOT[A] · C) + (B · C) = (A · B) + (NOT[A] · C)	A · (B + C) = (A · B) + (A · C)
(11)	NOT[A + B] = NOT[A] · NOT[B]	NOT[A · B] = NOT[A] + NOT[B]	De Morgan's theorem