Question

Hey...can anyone please explain how I figure out if ~(p ^ q) is equivalent or not equivalent to ~p ^ q

Answer 1

I believe you can use a truth table to check this. Make a truth table for each and see if they are the same.

Answer 2

It isn't the equivalence of ~(P ^ Q) would be ~P \/ ~Q according to DeMorgan's law.

Answer 3

does ^ = logical OR and \/ = logical AND?

Answer 4

^ is and
\/ is or

Answer 5

^ is the "and" and V is the "or"

Answer 6

I was thinking it was what zealhack was saying...but I always confuse myself!!

Answer 7

you can make a truth table. check each combination of true and false like this:

p = true, q = true:
~(true ^ true) = ~(true) = false
p = true, q = false:
~(true ^ false) = ~false = true

and so forth. make sense?

Answer 8

there will be 4 rows for each table (TT, TF, FT, FF). if the two tables are identical then the statements are equivalent.

Answer 9

right, this all makes sense

Answer 10

so in the first column of answers it would end up being T, F, F, F...right?

Answer 11

for which statement?

Answer 12

wouldn't that just mean the number has to be 5 or bigger?

Answer 13

there are no numbers per say. these are logical expressions. each p, q can only be either true or false.

Answer 14

heisenberg...right, I was helping another girl (trying to) and it popped up on here...sorry about that. The statement I was figuring out was the first one: ~(p ^ q)