Testing whether Argument is valid or not I am to determine if argument is valid by making truth table

ATTEMPT
Let 
W= Warning lights will come on
P= Pressure is high
R=Relief valve is clogged  
Then i have premises as 
W $\leftrightarrows$ P AND R ,where the symbol indicates bi conditional statement (1st Premise)
Negatition R                         (2nd Premise)
Therefore W $\leftrightarrows$  P   (Conclusion)

Now i made truth table as usual with 8 rows and written all other stuff. In first row where W,P,R are false , the premises and conclusion is coming out to be true which makes argument valid. But textbook states that it is invalid. I would like to know where i am going wrong
Thanks
 A: The claimed conclusion is not $W\leftrightarrow R$ as you wrote but rather it is $W\leftrightarrow P$. From the given $\neg R$ we can conclude that $P\land R$ is false and hence the equivalent $W$ is also false. If the claim were correct,we could infer $\neg P$, but we certainly can't.
Incidentally, your mistake in encoding the claim as $W\leftrightarrow R$ does give a valid conclusion: As seen above, $W$ is false and as both $W$ and $R$ are false, $W\leftrightarrow$ is true.
A: I don't see why you want to solve your problem using the truth table.


*

*Firstly, here is an intuitive approach that I believe the first thing to do when you have such problems. 


$$ ``\mbox{Warning lights is on}" \Longleftrightarrow ``\mbox{Pressure is high}" \wedge  \ `` \mbox{Relief valve is clogged }" $$
is equivalent to : 
$$ ``\mbox{Warning lights is } \color{#C00}{off} " \Longleftrightarrow `` \mbox{Pressure is } \color{#C00}{not} \mbox{ high}" \vee  \ `` \mbox{Relief valve is } \color{#C00}{not} \mbox{ clogged }" \tag{P} $$ 
Now, we consider the statements $(P)$ to be true and that $``\mbox{the Relief valve is not clogged}"$, that implies that Warning lights is off ( regardless of the pressure).
So the conclusion is obviously invalid (because the pressure can be too hight and the warning still off).


*

*Now if  the table is required by the question, you have to add an arrow in your table that contain the truth values of 


$$ \left( (W \Longleftrightarrow  R \wedge P) \wedge \lnot R \right) \Longrightarrow \left( W \Longleftrightarrow P \right) $$
