Question

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement.

[(~p V ~q) ^ ~q]
true
false

Answer 1

If p is true, then ~p is false. So ~p = F
If q is false, then ~q is true. So ~q = T
If r is false, then ~r is true. So ~r = T

[(~p V ~q) ^ ~q]


[(F V T) ^ T]


[T ^ T]


T


So the truth value of the compound statement is true.

Answer 2

notes: p v q is true if either p or q is true. Also, p ^ q is only true if BOTH p AND q are true.

Answer 3

that makes sense. :)

Answer 4

ie 1 line of the truth table (the second)

http://www.wolframalpha.com/input/?i=%28%28%C2%ACp%29+or+%28%C2%ACq%29%29+and+%28%C2%ACq%29%29+