Understanding Truth Values of Basic Logical Statements. I'm starting a course in proofs and our first two chapters have been on set theory and logic, both of which I have understood to an extent. However, one of my homework questions asks me the following and I'm not quite sure what I'm being asked to do.
Suppose the statement $((P\land Q)\lor R)\Rightarrow(R\lor S)$ is false. Find the truth values of said variables.
In English, I believe the above claims that to say that "if either P and Q or R, then either R or S" is false. Am I being asked to find which combinations of P, Q, R, and S satisfy the above statement, or something else entirely?
I apologize in advance for resorting to asking a homework question on MSE but it's the only one I haven't finished and I'd like to know how to approach a question like this if it were to be on a quiz tomorrow. 
 A: Don't worry, I struggled with this myself and Math SE has offered me good solutions, so I'll give the same help to you.
$((P \wedge Q) \vee R) \Longrightarrow (R \vee S)$ is false when $((P \wedge Q) \vee R)$ is true and $(R \vee S)$ is false. And $((P \wedge Q) \vee R)$ is true when P and Q are true and when R is either true or false. So if the whole statement is false, then $(R \vee S)$ is false, and so $R$ must be false and $S$ is false as well.
and you get
   T                  F

$((P \wedge Q) \vee R) \Longrightarrow (R \vee S)$
The whole statement is false
Because:
\begin{array}{C|C}
p & q & p \Longrightarrow q \\
\hline
T & T & T\\
T & F & F\\
F & T & T\\
F & F & T
\end{array}
A: Since you're doing proofs:
$((P \land Q) \lor R) \to (R \lor S) \equiv$
$(R \lor S) \lor \lnot ((P \land Q) \lor R) \equiv$
$(R \lor S) \lor (\lnot (P \land Q) \land \lnot R) \equiv$
$(R \lor S) \lor ((\lnot P \lor \lnot Q) \land \lnot R) \equiv$
$(R \lor S \lor \lnot P \lor \lnot Q) \land (R \lor S \lor \lnot R) \equiv$
$(R \lor S \lor \lnot P \lor \lnot Q) \equiv$
$\lnot (\lnot R \land \lnot S \land P \land Q)$
Is false precisely when $\lnot R$, $\lnot S$, $P$ and $Q$.  I find that there is frequently an easily-interpretable form for most logic statements somewhere along the way to converting to either CNF or DNF.
