In propositional logic we had studied the following rules:
(P • Q) -> P, Q ~(P ∨ Q) -> ~P, ~Q ~(P ⊃ Q) -> P, ~Q
and say, the inference rules:
~(P • Q), P -> ~Q (P ∨ Q), ~P -> Q (P ⊃ Q), ~Q -> ~P
Now in predicate logic you can use these rules but my question is how do I decide where does the negation go? This is unfortunately not clearly stated in the book.
If I have:
~((x)Pa ⊃ (x)Qa)
I can deduce two inferences from this such as firstly:
But for the second inference where does the negation go?