Question

State and define the principle of duality. Why is it so important in Boolean Algebra?

Answer 1

Principle of duality: Duality principle states that from every boolean relation another boolean relation can be derived by:

1. Changing each OR sign (+) to an AND sign (•)

2. Changing each AND sign (.) to an OR sign (+)

ex : Dual of A + A’B = A . (A¹ + B)

Importance in Boolean Algebra: The principle of duality is an important concept in Boolean algebra, particularly in proving various theorems. The principle of duality is used extensively in proving Boolean algebra theorem. Once we prove that an expression is valid, by the principle of duality, its dual is also valid. Hence, our effort in proving various theorems is reduced to half.