I don't want to sound negative, but it's usually unhelpful to treat the goal of patent-claim design by analogies that look like a mathematical exercise in something like set theory.
The business goal is to have the claims directly cover
(a) whatever is planned to be the subject of trade in the invention, e.g. whatever forms of invented product/process/'embodiment' are going to be sold or otherwise traded, and
(b) any other product (&c) that would effectively use enough of the patented invention to compete with (a).
(A mention in passing: if other envisaged products would compete just as well even where they use nothing of the invention, it's time for a re-think. Maybe the invention isn't worth patenting after all: but on the other hand, perhaps the envisaged alternatives, if new, could even represent a further invention that should be patented as well!)
At the same time, as is well known, the claims must not cover anything that is part of the prior art or is in any way citable against the claimed invention.
It can occasionally be helpful to think of the problem of claim design as not unlike like the encircling game of 'go' -- with areas of categories that need to be covered, and other areas that must not be covered.
But in addition, there is a further legal goal, that the claims actually define an invention (and not just some random collection of features). The claims should point out, at least in general terms, a useful thing effected by the claimed collection of features. This is also why an invention consisting of some A, B and C can't in general be effectively claimed just by A and B, or even by A alone -- except in special cases where the missing essential element can be understood as implied by the claim. Outside those special cases, subcombinations are likely to cover inoperative things, thus, not patentable invention. (If on the other hand, some A+B's that can be envisaged are actually operative and useful for the invention's purpose without any C, then this demands another urgent re-think about what the invention really is: and a serious re-draft that should take place before filing the application!)
Not only that, but one wants to have a graded set of claims: the broadest of them as described above, and others carefully delimited to include subgenerically useful features. The aim here is to build in advance a second line of defense against the possibility -- far from unlikely -- that some further prior art should turn up in the future, something that turns out to be fatal for the broadest claims initially made. Then, the subgenerically useful claims may (hopefully) turn out to be of a kind that has the best chance of being still patentable against the sum of the previously-known and newly discovered prior art, at the same time retaining a useful scope so that the remaining claims still cover the core product and as far as possible its similars.
If you think that this is an impossible demand for clairvoyance, well perhaps it is: but it shows the nature of the problem that calls for solution when drafting patent descriptions and claims -- and sometimes for the luck that can favor a prepared drafting mind.
Much of the reason why all of this is necessary is an artificial reason: that the law in general allows amendments of the scope of the claims in one direction only -- to give up part of the scope of protection originally described and claimed. (The US law, but few if any others, allows -- within a time limit -- to add or broaden claims to include initially unclaimed subject-matter, provided that the resulting claimed subject-matter was originally present in the application and sufficiently described.) There is in general no legal opportunity, after submitting the application, to get nearer the truth of the invention (so to speak) by redefining the claims later to embrace anything inadvertently left absent from the whole application i.e. description and claims as first submitted.
(This legal one-way path can be seen as in some ways unfair. But irrespective of that, the result of it is a strong tendency in practice towards broad-as-possible claiming at the outset. In turn, the results of that can lead to complaints of overclaiming and abuse of the system -- complaints sometimes also reasonable in their turn.)
In any event, the scenario painted in the question, of a hypothetical set of elements A, B and C, is almost always going to be seriously inadequate to the description of any invention. Any three elements are susceptible of alternative decriptions, A', B' C'; A", B", C", &c, practically ad infinitum. How each element is described, and how well its essential features, forms, functions and attributes are captured in language, is always going to be crucial to the effectiveness (or otherwise) of any patent rights obtained.
That's why I suggested at the outset that this is not a problem in set theory. It involves suiting the language of description to the new thing at hand, in several ways -- generically; as economically as feasible; and well enough to capture and make explicit the forms, functions and results.
I hope this may be somewhat helpful, even though the problems can be difficult!