Boolean algebra - dual function and self dual function

Question

I'm having a problem understanding what influences the dual function has on the original function output.

For example, if I have a self dual function - for the input 11 the function out put will be 1, and the output of the dual function will be the same.

Now for dual function - I saw on the Internet that the dual function always give the opposite output compare to the original function. Im pretty confused because if we look on the function A*B Then the dual function is A+B. now for the input A=1,B=1 they giving the same output.

Some one can explain me what dual function is beside changing the operators?

Thanks!

Answer 1

Dual function simply implies to change an expression to its opposite logic I.e changing negative logic to positive logic and vice versa. By negative logic, I mean logic where high means 0 and low means 1. By positive logic, I mean logic where high means 1 and low means 0.

Dual function of an expression is simply obtained by exchanging OR operator to AND and AND to OR.

Sometime dual function of an expression results in same expression. For example F=AB+BC+AC

Talking about A*B, A+B is surely dual function of it. Output should be opposite, as I said dual function mean changing logic(positive to negative or negative to positive). During changing operators, change your input also (1 to 0 or 0 to 1)