You don't seem to have any comprehension at all of what I am doing! I am building a model of an explanation of the elements of set A. B is a mental construct! It is "defined" to be a finite unordered set of elements of A.
My model is very simply that some elements of A are available to me and I am calling that collection of those elements B. That is, some information about whatever it is that I am trying to explain or understand is available to me. Here I am taking the terms "explain" and "understand" to be equivalent in the sense that, if you cannot explain something, you must not understand it and, from the other side of the coin, if you do not understand something you certainly are not qualified to explain it.
If you had questioned the existence of B, your question could at least be considered rational; however, if you understood what I was doing, you would comprehend that, even if B vanishes, my modeling approach is still valid. As B is that part of A which is available to be used in solving the problem, if B vanishes, it merely means then what you have to work with contains no elements of A whatsoever certainly a circumstance which is possible (from my experiance, a phenomena actually relatively common to a lot of psudo thinkers).
If it is your intention to explain something from the perspective that nothing from it is available to you, it should be clear to you that any explanation you come up with is a total figment of your imagination. This is apparently a position taken by some people but I am personally of the opinion that such a step constitutes an unsupportable assumption and is a step which should not be taken.
I think you referred to such people as "anti-realists". If you understand what I have said above, you should understand that my model applies just as well to both cases (realism and anti-realism) and the truth of my deductions does not depend the existence or non-existence of A. As an aside, if B vanishes (i.e., no possible collections of elements of A exist or can exist) then I think most rational people would deduce that A does not exist.
Have fun -- Dick