Some someple question about GATES(electrical)

[extreme]

I recently came across this
A(A+B)=A
why is it so???
it's according to absorption theorem.
and according to booelean allgebra theorem
i wanna ask what is the difference between dual expression and valid expression..

[wawa]

if A + B is the entire set,
then A + B = 1
so A(1) = A

[extreme]

if A + B is the entire set,
then A + B = 1
so A(1) = A

in my opinion the result would still be influenced by the gate B so if A is zero be is 1 the result may still be 1.... but then it it proven somewhere in electronic book though i don't really bother to search for it.