Doubt in self-dual boolean function

Question

For a function to be self-dual, f= dual of f

Defination in my class gives me that for dual, i need to replace and with or and variables remains same. But in following post, defination of self-dual function is given as follows -

What is the number of self dual boolean functions?

the classical definition of self-dual boolean function is a function that commutes with the permutation 0/1 (i.e. negation ¬), precisely: $f(x1,...,xn)=¬f(¬x1,...,¬xn)$.

But in above defination, variables are replaced with complement of terms(which i think is not so in dual?). Please any one clarify my doubt.

Answer 1

The $\land$ and the $\lor$ are each other's dual in the sense that $P \land Q = \neg(\neg P \lor \neg Q)$ ... and therefore also $P \lor Q = \neg(\neg P \land \neg Q)$. So the post you found has the correct definition.

I think that you may be thinking: "But isn't it that $P \land Q$ is the dual of $P \lor Q$? ... So where are the negations?" ... but that is not the way to think about this: you just say that the $\land$ is the dual of $\lor$