Laws and theorems of Boolean algebra

Operations with 0 and 1
1.x+0=x               x.x=x
2.x+1=1               x.0=0
Impotent laws
3.x+x=x               x.x=x
Involution law
4.(x')'=x
Laws of complementary
5.x+x'=1               x.x'=0
Associative law
6.(x+y)+z=x+(y+z)                 (xy)z=x(yz)=(xy)z
Distributive law
7.x(y+z)=xy+xz                      x+(yz)=(x+y)(x+z)
simplification theorems
8.xy+xy'=x
9.x+xy=x
10.(x+y')=xy