Laws of Boolean Algebra

Different Laws of Boolean algebra

Different laws of Boolean algebra are:
Identity Law:
“Output is same as the input when input is sum with 0 and and product with 1.” i.e.
(i) A*1 = 1
(ii) A+0 = A

Complement Law:
“Sum of input and its complement is always 1 and product of input and its complements is always 0.”
The Complement law of Boolean algebra is expressed by :
a. A+A’= 1
b. A.A’ = 0

Commutative Law:
“Changing the sequence of the variables does not have any effect on the output.”
This law is expressed by :
a. (A+B) = (B+A)
b. (A*B) = (B*A)

Associative Law:
“The order in which the logic operations are performed is irrelevant as their effect is the same.”
This law is expressed by :
a. (A+B)+C = A+(B+C)
b. (A*B)*C = A*(B*C)

Distributive Law:
Distributive law states the following condition.
a. A*(B+C) = A*B + A*C
b. (A*B)*C = A*(B*C)

Boundedness Law:
Boundedness law states the following condition.
a. A+1 = 1 b. A.0 = 0

Idempotent Law:
Idempotent law states the following condition.
a. A+A = A
b. A.A = A

Absorption Law:
Absorption law states the following condition.
a. A+(A.B) = A
b. A.(A+B) = A

Inversion/Involution Law:
This Law use the NOT operation. The inversive law states that double inversion of a variable results in the original variable itself.
i.e a. (A’)’ = A