%% propositional dualities: 15 points proof deMorganNotOr : ~(A | B) => ~A & ~B proof deMorganOrNot : (~A | ~B) => ~(A & B) proof deMorganNotAnd : ~(A & B) => ~A | ~B proof deMorganAndNot : (~A & ~B) => ~(A | B) %% quantifier dualities: 15 points proof deMorganNotEx : ~(?x:t. A(x)) => !x:t. ~A(x) proof deMorganExNot : (?x:t. ~A(x)) => ~!x:t. A(x) proof deMorganNotAll : ~(!x:t. A(x)) => ?x:t. ~A(x) proof deMorganAllNot : (!x:t. ~A(x)) => ~?x:t. A(x)