Is ~(p v q) true or false?

Question

Am I supposed to distribute whats in the parenthesis? If not, then is it just the opposite of the true/false in the parenthesis?

Sorry if I sound so confusing ^_^;

Thanks so much :)

Answer 1

Actually, this has a variety of answers depending on what p and q are.

1. If p is true and q is true then p U q is true and not (p U q) is False
2. If p is false and q is true then p U q is true and not (p U q) is False
3. if p is true and q is false then p U q is true and not (p U q) is False
4. if p is false and q is false then p U q is false and not (p U q) is True

Answer 2

No problem at all.

You negate each term in the parentheses, but you also MUST switch the sign. If it's V, as it is in this case, it becomes ^ (the "and" symbol).

So, this problem becomes:
~p ^ ~q

And you evaluate that.

Hope that helps. =)

(P.S. That is called De Morgan's Law)

Answer 3

Do the parentheses first, then take the opposite.

Answer 4

r = ~(p V q)

if p V q = true then
r = false
else
r = true

it can be done either as
~(p V q)
or as
~p ^ ~q