given p is true, q is true, and r is false, find the truth value of the statement ~q -- (p ^ ~r)

Question

given p is true, q is true, and r is false, find the truth value of the statement ~q --> (p ^ ~r)

kinggeorge · Answer

First, what's the truth value of the statement (p ^ ~r)?

anonymous · Answer

true

kinggeorge · Answer

Let's call that s. So the value of s is true. Now what's the truth value of (~q --> s)?

anonymous · Answer

true!

anonymous · Answer

has to be true --> false to get a false, correct?

kinggeorge · Answer

Correct. Since (~q-->s) was true, the statement is true.

anonymous · Answer

great. so a truth table isn't needed for this one?

kinggeorge · Answer

It's not necessary since you're already given the truth values, but making one might allow you to see the answer very easily. 

If you were to make the table, you would then have to pick out the row that has p=TRUE, q=TRUE, r=FALSE, and find the value at the other end of the table.

anonymous · Answer

ok. thanks!

kinggeorge · Answer

You're welcome.

anonymous · Answer

typing next one.