Can someone help me prove De Morgan's Law. In my logic class we are using a very basic set of rules for derivations and I can't for the life of me figure out how to prove the law with them. It's not homework; my TA gave me extra problems to practice for the midterm. By the way, I know this article is asking the same question, but I do not understand the notation so I don't know if they're restricted to the same rules.
Prove p&q <-> ~(~pV~q) and/or pvq <-> ~(~p&~q) using only these rules: &Intro/Elim, vIntro/Elim, ~Intro/Elim, ->Intro/Elim, <->Intro/Elim. Please use this notation as well.
As far as I can tell, the proof should look like this:
|pVq Hyp |- ||~p&~q Hyp[for ~Intro] ||- ||~p &Elim[~p^~q] ||q **I'm not sure how to prove that ~p -> q with the limited rules** ||~q &Elim[~p^~q] |~(~p&~q) ~Intro[~p&~q, q, ~q]