SOLUTION: Hello. I am looking for assistance on this particular problem. ANy help you can give is greatly appreciated. Let p represent a true statement, while q and r represent false statem

Algebra ->  Conjunction -> SOLUTION: Hello. I am looking for assistance on this particular problem. ANy help you can give is greatly appreciated. Let p represent a true statement, while q and r represent false statem      Log On


   

Question 470593: Hello. I am looking for assistance on this particular problem. ANy help you can give is greatly appreciated. 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]

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If p is true, then ~p is false since ~p is the opposite of p. Note: ~p means "not p"


If q is false, then ~q (not q) is NOT false, so ~q is true.


So we know that ~p is false and ~q is true. So ~p v ~q is then true because p v q is true if either p or q is true.


Finally, (~p v ~q) ^ ~q is true because BOTH ~p v ~q AND ~q are true. Since they are BOTH true, the conjunction is true.


So (~p v ~q) ^ ~q is true, which is the final truth value.


Note: I noticed that you mentioned r, but it doesn't show up in the expression. Is that a typo?