How do I find the truth value in this logic problem: $(( p \lor s) \land \neg q) \rightarrow ( r \rightarrow s)$? The problem is as follows:
$$[\left ( p \vee s\right) \wedge \sim q\,] \rightarrow \left ( r \rightarrow s \right )$$
From the preceding statement find the truth value of $\textrm{p, q, r, s}$
The alternatives in my book are the following:


*

*TFTF

*TTFT

*TTTF 

*TFFT 

*TFFF


However I'm confused exactly how do I get to any of those answers.
I tried to build up a truth table to get the answer, since the number of combinations for the four different variables would mean $2^{4}=16$.
The sketch of the table what I build is shown below:

The process was tedious and I'm not sure if the result it is correct but the thing is I don't know if this is what it is being asked. Is there any way to reduce this table to any of the alternatives given?
I have forgotten exactly if there is a way to solve this problem without resorting with this approach or any shortcut?
Can somebody help me to find the right answer or to guide me what to do?.


The problem is as follows:
$$[\left ( p \vee s\right) \wedge \sim q\,] \rightarrow \left ( r \rightarrow s \right )$$
From the preceding statement find the truth value of $\textrm{p, q, r, s}$

Your truth table is incorrect. Try this truth table generator: http://web.stanford.edu/class/cs103/tools/truth-table-tool/
Hint: From its truth table, your statement is true for all combinations of truth values for p, q, r, s except for p=T, q=F, r=T and s=F.
