What are the basic postulates of boolean algebra?

Q. What are the basic postulates of boolean algebra?

Answer :-

A modern algebra which uses the set of numbers 0 and 1, and consists of three basic operations OR, AND and NOT.

 
 
 
 
	 

 
 
 
	 
1.
 
	 
Properties of 0
 
	 
0 + X = X;    0.X=0
 
 
 
	 
2.
 
	 
Properties of 1
 
	 
1 + X = 1;     1.X = X
 
 
 
	 
3.
 
	 
Indempotence law
 
	 
X + X = X;     X.X = X
 
 
 
	 
4.
 
	 
Involution
 
	 
(X’)’=X
 
 
 
	 
5.
 
	 
Complementarity law
 
	 
X + X’ = 1;    X. X’ = 0
 
 
 
	 
6.
 
	 
Commutative law
 
	 
X+Y=Y+X;    X.Y = Y.X
 
 
 
	 
7.
 
	 
Associative law
 
	 
X+ (Y+Z)=(X+Y)+Z;   X(YZ) = (XY) Z
 
 
 
	 
8.
 
	 
Distributive law
 
	 
X(Y+Z)= XY + XZ;   X + YZ = (X+Y)(X + Z)
 
 
 
	 
9.
 
	 
Absorption law
 
	 
X + XY = X ;   X. (X+Y)= X
 
 
 
	 
10.
 
	 
Other (3rd distributive law)
 
	 
X+X’Y=X+Y