UNIT 1 COMPUTER SYSTEM PRINCIPLE OF DUALITY IN BOOLEAN ALGEBRA
Q: Define the principle of duality in boolean algebra
The principle of duality in Boolean algebra states that any theorem or algebraic operation in Boolean algebra remains valid if the operators AND (·) and OR (+) are interchanged, and if 0 and 1 are swapped. In other words:
1. If an expression is true for AND operations, it will also be true if you replace all AND operations with OR operations, and vice versa.
2. If an expression is true when evaluated with 0 representing false and 1 representing true, it will also be true if you swap 0 and 1.
Mathematically, if A and B are any two Boolean variables, then the principle of duality implies:
1. The dual of (A · B) is (A + B).
2. The dual of (A + B) is (A · B).
This principle is extremely useful in simplifying Boolean expressions and proving theorems, as it provides an alternative perspective to solve problems and verify results.
Comments
Post a Comment