Logic Validity Question with Many Variables Is the following valid?
Premises: I either eat a burger or pasta. 
If I eat a burger I will have a milkshake.
If I eat pasta I will have water.
I do not have water. 
Conclusion: I ate a burger
I think it is valid if we can assume that in this universe the only options are a burger and pasta. Can we assume then that those are the only 2 options available or is it possible that I don't have water so I could have a different meal not listed here?
Thanks in advance!
 A: There may be more options in this particular restaurant, but the first premise says that you (for whatever reason ... maybe it's food allergies or who knows what) will have either the pasta or the burger. And, since we can rule out you having the pasta (because then you would have the water, which you don't), we know that you will have the burger. So, even if other people can have some third option without having the water, we know that you will definitely have the burger. So, the argument is valid, independent of whether there are other options at this restaurant or not.
A: Your reasoning is correct. Whether or not you can conclude that you ate a burger depends on the specification of the universe.
Whether you should assume the universe is limited to those two main courses depends on the context. It's often implicit in these kinds of artificial problems. If you encounter this kind of question on an exam the appropriate answer would be "it depends" - for exactly the reason you provide.
A: $P = $eat a hamburger
$Q = $eat pasta
$R =$ I will eat a shake
$ S =$ I will have water
Then :
1.- $P\vee Q$
2.- $P\Rightarrow R$
3.- $Q\Rightarrow S$
4.- $\neg S$
5.- MT(3,4) $\neg Q$
6.- DS(1,5) $P$
