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Resolution method and counterexample


New member
Dec 16, 2018
Am new to this forum, but I have looked around here for some time now, since am studying a course of logic in the context of computer science. I have a very important exam in a few days, and while I thought I got it, I got shocked when I was looking on previous graded exams to see what I could work on in the final days. And when I came to the part about resolution method and counterexamples for predicate logic on one exam I realised that either there is something I don't understand, or they actually gave me a bad exam (It's supposed to be highest grade).

The picture look kinda bad since I changed a few words on my native language manually and had to refit it for the upload. So just ask if there is something I can clarify.
The question on the exam is as follows:
"Is the following true? If it is, then show that with the resolution method, if it is not true then show that with a counterexample."
You can see the sub-questions A and B and under that the answers to each sub-question in the picture.
One thing I don't get if this is actually correct is that when doing resolution method you don't have to use all parts of the conclusion? In this case only \lnot q(a) is used and not \lnot s(a).
Other than that I get sub-question A. With B I first of all cant see why it wouldn't be possible to use only {a} to make a counterexample? And second it looks to me as q(b)=1 kind of negates the premise?


I would be extremely grateful if someone could help me understand. I really want to get this and it is also hugely important for my studies.

With kind regards