To negate a formula F, it is sufficient to put ~ before it: ~F.
To negate this you need to first simply the given, it makes it easier...
So ~(~p v ~q) = p AND q.
NOW, the negation of the above is ~p v ~q
The second part is p A q. so the negation of that is ~p or ~ q.
When you put the two together you get...
~p v ~q <-> ~p v ~q
thanks but im a little confused!! When it says to negate a proposition doesnt it mean put brackets around the whole proposition and then negate that using the laws of negation..? thats what I did for my answer..but that first negation sign doesnt seem to be touched if the negation for , leaving p = untouched..
I said this with tongue in cheek. In fact, I still don't understand what you problem asks. To negate a formula F means to write the negation of F, which is ~F. I am not sure if is the whole formula you need to negate, or if you need to prove this formula by negating one part. Or maybe you need to negate the whole formula but transform the result in such a way that negations ~ occur only before propositional variables... Please state your problem more precisely.To negate a formula F, it is sufficient to put ~ before it: ~F.
I made a lil mistake, but i just fixed it, in my post above....
In order to negate, like you said, you CAN put brackets around the entire proposition and then apply the laws of negation.
Are you suppose to negate [ (~p v ~q) <-> p A q ] or [~(~p v ~q) <-> p A q] ????
If the second option is what you are suppose to NEGATE then my post above should work. I applied the laws of negation to that, like you said. Be careful when negating And and OR signs.
For example:
(p v q) <---- negation of= ~p AND ~q
(p A q) <--- negation of= ~p OR ~ q