The commutative law allows change in position of AND or OR variables. There are two commutative laws.
(i) A + B = B + A
Thus, the order in which the variables are ORed is immaterial.
(ii) A ⋅ B = B ⋅ A
Thus, the order in which the variables are ANDed is immaterial.
This law can be extended to any number of variables.
Associative Laws
The associative law allows grouping of variables. There are two associative laws
(i) (A + B) + C = A + (B + C)
Thus, the way the variables are grouped and ORed is immaterial.
(ii) (A ⋅ B) ⋅ C = A ⋅ (B ⋅ C)
Thus, the way the variables are grouped and ANDed is immaterial.
This law can be extended to any number of variables.
Distributive Laws
The distributive law allows factoring or multiplying out of expressions. There are two distributive
laws.
(i) A(B + C) = AB + AC
(ii) A + BC = (A + B) (A + C)
This law is applicable for single variable as well as a combination of variables.
Idempotent Laws
Idempotent means the same value. There are two Idempotent laws
(i) A ⋅ A = A
i.e., ANDing of a variable with itself is equal to that variable only.
(ii) A + A = A
i.e., ORing of a variable with itself is equal to that variable only.
Absorption Laws
There are two absorption laws
(i) A + AB = A(1 + B) = A (ii)A (A + B) = A
Involutory Law
This law states that, for any variable ‘A’
A = (A′)′ = A
