Find an equivalent to $(P \lor Q) \land (P \to R) \land (Q \to S)$ I need some help regarding solving a logic. The question is to find an equivalent to the following logic.
$$(P \lor Q) \land (P \to R) \land (Q \to S)$$
The choices are

(a) $S \land R$
  (b) $S \to R$
  (c) $S \lor R$
  (d) none of these

The answer given in the book is (c) $S \lor R$ . I tried many ways, but unable to bring the solution. So, kindly explain me the steps. Thanks in advance.
 A: The solution is (d)
The first formula is false if $P$ and $Q$ are false, but all other answers (a), (b) or (c) can be true if $P$ and $Q$ are false (by setting $R$ and $S$ true for example).
EDIT :
$$(P\vee Q)\wedge (P\rightarrow R) \wedge (Q\rightarrow S)$$
$$\Leftrightarrow$$
$$(P\vee Q)\wedge (\neg P\vee R) \wedge (\neg Q\vee S)$$
And you can't just eliminate $P$ and $Q$ to obtain an equivalent formula. However, you can eliminate them if you just try to find an implication...
$$((P\vee Q)\wedge (\neg P\vee R)) \wedge (\neg Q\vee S) \Rightarrow (Q\vee R) \wedge (\neg Q\vee S) \Rightarrow (R\vee S)$$
A: You can see that the implication $(P \lor Q) \land (P \to R) \land (Q \to S) \Rightarrow (R \lor S)$ is intuitively clear without resorting to truth tables. 
Let $P$ be the statement: "We are in the Phillipines."
Let $Q$ be the statement: "We are in Quebec."
Let $R$ be the statement: "It is raining."
Let $S$ be the statement: "It is snowing."
The expression $(P \lor Q) \land (P \to R) \land (Q \to S)$ then becomes:
We are in the Phillipines or Quebec, and if we are in the Phillipines then it is raining and if we are in Quebec then it is snowing. Clearly then, it is either raining or snowing. $(R \lor S)$
A: This is not an equivalence but rather a valid argument. In symbols it looks like
a) $P\vee Q$
b) $P\rightarrow R$
c) $Q\rightarrow S$

$\rightarrow R\vee S$
To see the implication is valid argument consider the simpler statement
a) $P\vee Q$
b) $P\rightarrow R$

$\rightarrow R \vee Q$
This can be checked by a truth table.
