Set Interview Question, Any Creative Way to solve? I ran into a simple question, but I need an expert help me more to understand more: 
The following is True:
$ A - (C \cup B)= (A-B)-C$
$ C - (B \cup A)= (C-B)-A$
$ B - (A \cup C)= (B-C)-A$
and the following is False:
$ A - (B \cup C)= (B-C)-A$
this is an interview question, but how we can check the these sentence as true or false quickly?

In my opinion, in the case of only 3 sets, it is most straightforward to draw the corresponding Venn diagram

and find out the resulting subset when you apply the operations on both sides of your equalities. In an interview, I think it would show sense of intuition; you shouldn't be afraid of drawing little diagrams for simple math questions.
EDIT: After thinking about it, this is more about pragmatism than intuition. Here you won't have to find the right trick, or use too much brainpower, and you will be able to apply this even if put under the stress of the interview.
Which is not to say you won't find other answers helpful if you have to actually prove/disprove the predicates, or if you want to show that you are, in fact, able to find tricks.
