
Am I stupid or is this proof wrong?
Im probably wrong, but if A shares no elements with X, then X - A = X, and X - X = null set (?), so then x is a meneber of the null set (already makes no sense, but say that x is nothing or excuse it for now (is this where i went wrong?) and we get x is a member of X (this is technically true because null set is a subset of all sets but its not a member of them? Im very confused), and also x is not a member of X - A. But thats a contradiction because in the case they share no elements thats just X. So it says x is both a memeber of and not a member of X in this scenario? I have a feeling that I did something wrong.