Boolean Algebra, Duality Principle and `Huntington postulates.`

Lets start our Bollean Algebra discussions with 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.

Next lets discuss Huntington Postulates

P1. Postulate:- x + 0 = x.  Adding a number to 0 results in number itself.

`Next` From duality of P1

P2. Postulate:- x * 1 = x

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

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

P4. Postulate:- x * x’ = 0. From commutative property of binary numbers we have:

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

Refer Boolean Agebra Theorems from here

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