Question

s principle of duality making the entire Boolean algebra concept true? If yes, proof

it with an example.​

Answer 1

The principle of duality in Boolean algebra states that if you have a true Boolean statement (equation) then the dual of this statement (equation) is true. The dual of a boolean statement is found by replacing the statement’s symbols with their counterparts. This means a “0” becomes a “1”, “1” becomes a “0”, “+” becomes a “.” and “.” becomes a “+”.

Here’s an example of the principle of duality in Boolean algebra:

Suppose we have the following true Boolean statement (equation):

(a)   1 + 0 = 1

The dual of this statement is:

(b)    0 . 1 = 0

As we can see, the dual of the true Boolean statement (a) is (b). We found (b) by replacing each symbol from (a) with its Boolean counterpart as described above. Clearly, (b) is also a true Boolean statement.

The key takeaway from this principle is there is nothing intrinsically special about our denotation of “0” and “1”.