Laws followed in digital electronics

Laws followed by digital electronics :

Annulment Law :
if A (is unknown value, means whether 0 or 1) is AND'ed with 0 then result always equal to  0.
if A is OR'ed with 1 then the result always equal to 1.
                      A . 0 = 0
                      A + 1 = 1

Identity Law :
The result always equal to  A when  A is OR'ed with 0 or if A is AND'ed with 1.
                      A . 1 = A
                       A + 0 = A

Idempotent Law :
The result is always equal to A when OR'ed or AND'ed with  A itself.
                       A + A = A
                       A . A = A

Complement Law :
The result is always equal to 0 when AND'ed with complement of itself.
The result is always equal to 1 when OR'ed with complement of itself.
                       A . ABAR = 0
                       A + ABAR = 1

Commutative Law :
 The order of application of two separate  inputs is not important.
                         A + B = B+ A

Double Negation Law :

if A is two times complemented it gives same value.
                        complement (complement ( A) ) = A

de Morgan's Law:

Law1 : NOR'ed of two inputs is equal to  AND'ed of complement inputs.
Law2 : NAND'ed of two inputs is equal to OR'ed of complement inputs.
             complement (A + B) = complement(A) . complement(B)
             complement (A . B ) = complement(A) + complement(B)