I have a Boolean function, which looks like this:
$ f(x,y,z)= (x∨y∧\neg z)∨ y\rightarrow \neg(x\rightarrow z) $
I simplified it to this:
$ (\neg x ∧ \neg y )∨ (x ∧ \neg z) $
The questions that I need to answer is whether this function is monotone, linear and self-dual. I don't quite remember how to do this and googling didn't help much. Do I need the truth table for that? Even if I make it, which arguments do I look at? All $ x,y,z, \neg x, \neg y, \neg z $ or only the ones that I have in the function?
Thanks in advance.