I have been studying duality and I am confused at the point that how are the two linked.
For example in discrete mathematics we see $$ {\sim}(A \land B) = {\sim}A \lor {\sim}B. $$ But in Boolean algebra using the rules of Duality we see that $$ A\ \text{and } B = A\ \text{or } B. $$ My question is that are the concepts linked together and if so don't they prove each other to be wrong?
I hope this answer helps someone else who also like me is confused between the concepts of negation and Duality.
In the negation part, we see that the right hand side of the equation is equal to the left hand side of the same equation that is
∼(A ∧ B) = ∼A ∨ ∼B
but on the other hand, in duality if we take the example
A or 1 = 1
through duality we see that
A and 0 = 0
This does not mean that
A and 0
and
A or 1
are equivalent. It just means that they are both true and logically correct, ie duality helps us create new laws that are logically correct.