Premises:
Whenever Drug Y is administered, the patient gets better.
Whenever Drug Y is not administered, the patient does not get better.
Conclusion:
Drug Y causes the patient to get better.
Supposed correct answer:
False.
I believe it is true. The test is claiming I'm using a correlation = causation fallacy, but I'm not given the wording of the premises. If we assume the premises are 100% true, then in no situation can the patient get better without taking the drug. And in every situation the drug is taken, the patient gets better. This means without a doubt that the drug causes them to get better, even if it's indirectly so as a catalyst for something else.
Inductive reasoning, bitches. It works.
I hope I can explain why with 'logic' and the specific wording, the answer should be false.
Keep in mind, with logic you look purely at the sentence structure and definitions given, without any added information. That added information is something of a cognative bias - remember that in logic puzzles such as this, you can replace the details with anything, and if you're doing it right, you'll still have the same answers.
In this case, the details are 'drug Y is/is not administered' and 'the patient gets better/does not get better'.
Whenever A, B.
Whenever not A, not B.
A causes B. - this is false.
Here's a few (hopefully more) clear examples of why this logic does not follow -
Whenever someone wakes up, they want to relieve their bladder.
Whenever someone doesn't wake up, they don't want to relieve their bladder.
Waking up causes someone to want to relieve their bladder. (Sleeping, someone wants to stay asleep. A full bladder may wake a person, but the bladder did not fill because someone woke up)
Whenever a Catholic is given last rites, the person dies soon from an expected cause.
Whenever a Catholic is not given last rites, the person does not die soon from an expected cause.
Giving a Catholic last rights causes the person to die soon from an expected cause. (Last rites, if given, are a reaction to the observed process of dying. This process is independent of the last rights, and withholding them when they would be given cannot save a life, nor will giving them to a person not about to die cause their death)
Using A as giving a drug or not and B as getting better or not is especially entrapping in this form of logic test - humans DEEPLY believe in the power of drugs to cure... to the point of making placebos work.