Sorry for any confusion and for the delay in replying (it took me a while to find your comment!). What struck me about your question was division and multiplication: (A/B)C and A/(BC) I took to be the normal arithmetic application of division and multiplication, which applies to numbers rather than sets (at least, in my limited experience with sets); that's why I assumed A, B and C were just numbers, single elements within U. So my line of thought was that (A/B)C expands to AC/B, with C in the numerator formed by the product of A and C; while A/(BC) contains the product of B and C in the denominator, so the two expressions are different.
Since it's over 50 years since I studied mathematics you are probably more familiar with sets than I am, and perhaps it's possible to apply multiplication and division to whole sets (as in matrices, for example); but I personally don't know how it's done.
I would be interested to know if you had a different interpretation. Yes, I will willingly offer explanations you need, as long as I understand the subject. You only have to ask.