Boolean Algebra

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Duality Principle

The duality property of Boolean algebra state that all binary expressions remain valid when following two steps are performed:

Step 1 :  Interchange OR and AND operators.

Step 2 :  Replace all 1’s by 0’s and 0’s by 1’s

Huntington Postulates

Adding a number to ‘0’ :

P1. Postulate:- x + 0 = x, next From duality of P1

P2. Postulate:- x * 1 = x

Sum of a number and its complement from a Set is ‘1’

P3. Postulate:- x + x’= 1, next From duality of P3

P4. Postulate:- x * x’ = 0

P5. Postulate:- x + y = y + x
From duality of P5

P6. Postulate:- x * y = y * x
From distributive property of binary numbers we have:-

P7. Postulate:- x(y + z) = xy + xz
From duality of P7  

a+bc = (a+b)(a+c)