De-Morgan’s Theorem

DE-MORGAN’S THEOREM:

De Morgan suggested two theorems that form important part of Boolean algebra. They are,

1) The complement of a product is equal to the sum of the complements.

(AB)' = A' + B'

•      FIRST THEOREM

2) The complement of a sum term is equal to the product of the complements.

(A + B)' = A'B'

•      SECOND THEOREM

APPLICATION OF DEMORGAN'S THEOREMS:

Apply to any number of variables:

PRINCIPLE OF DUALITY:

Principle of Duality theorem says,

·              Changing each OR sign to an AND sign

·              Changing each AND sign to an OR sign

·              Complementing any 0 or 1 appearing in the expression