Given the following question:
We are given two statements:
If the TV is too loud, then it will give me a headache
If I have a headache, then I will have to rest
Law of syllogism is a logical argument that derives from two statements which are assumed to be true.
If the TV is too loud then I will have to rest is not a logical argument since the TV isn't the cause of the person having to take a rest.
If I rest, then I have a headache isn't a logical argument speaking how a person doesn't have to rest because they have a headache.
If I rest, then the TV volume is too loud isn't logical at all.
If I have a headache, then the TV volume is too loud, is indeed a logical statement speaking how the first statement is IF the tv is too loud, then it will give me a headache. So it saying I have a headache, because the TV volume is too loud looking at the prior statements it is a logical conclusion.
Your answer is the fourth option.