given p is true, q is true, and r is false, find the truth value of the statement ~q --> (p ^ ~r)
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First, what's the truth value of the statement (p ^ ~r)?
Let's call that s. So the value of s is true. Now what's the truth value of (~q --> s)?
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has to be true --> false to get a false, correct?
Correct. Since (~q-->s) was true, the statement is true.
great. so a truth table isn't needed for this one?
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.