In my opinion a lot of these puzzles are about empathy toward the examiner as they generally ask variations of "what would I answer to this question?".

In the case of a logician and the properties of the elements of the empty set the frame of mind of the examiner is probaly going to be about using algebraic logical connectives.

For another nice example I can quote [0] via [1]

> Luria: All bears are white where there is always snow. In Novaya Zemlya there is always snow. What color are the bears there?

> Peasant: I have seen only black bears and I do not talk of what I have not seen.

> Luria: What what do my words imply?

> Peasant: If a person has not been there he can not say anything on the basis of words. If a man was 60 or 80 and had seen a white bear there and told me about it, he could be believed.

This is a more extreme case, but in my opinion it is the same phenomenon of being asked to take external things as true and work on them.

[0] https://languagelog.ldc.upenn.edu/nll/?p=481

[1] https://www.astralcodexten.com/p/somewhat-contra-marcus-on-a...