Electrical Engineering ⇒ Topic : Duality Theorem

Duality Theorem

With the help of duality theorem one can derive another Boolean relation by

• changing each OR sign to an AND sign,
• changing each AND sign to an OR sign and
• complementing any 0 or 1 appearing in the expression.

From Rule 1, A + O = A

                    A  . 1 = A

The dual property is obtained by changing the OR sign to an AND sign and by complementing the 0 to get a 1.

The duality theorem produces a new Boolean relation. For example, distributive law states that

                   A (B + C) = AB + BC

Changing each OR and AND operation, we get the following dual relation:

                   A + BC = (A + B)(A + C)