double negation rule - properties of semantic equivalence I know the rule for double negation is 
¬(¬P) ≡ P

However if I have:
¬(¬P V Q) 

does that give me
(P V Q)

or would the negation still apply to the Q:
(P V ¬Q)  

Thank you in advance.

NO.
In : 

$¬(¬P \lor Q)$ 

we have not a case of double negation, because the outer $\lnot$ applies to all the sub-formula inside the parentheses.
We have to apply De Morgan's laws to transform it into the equivalent form :

$\lnot \lnot P \land \lnot Q$

and then apply *double negation to get :


$P \land \lnot Q$.


