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?

To think through things quickly, you can see that $A-(C\cup B) = (A-B)-C$ is true, because on the left, you're taking a set $A$ and getting rid of anything in either $C$ or $B$, while on the right, you're taking $A$, first getting rid of anything in $B$, and then getting rid of anything in $C$.  The next two are similar (so similar, in fact, that it would slow me down wondering why they would, in effect, ask the same question three times in a row).  Finally, $A-(B\cup C)=(B-C)-A$ has to be false (in general) because on the left you only have stuff in $A$ while on the right you're getting rid of $A$.
Note, none of this constitutes rigorous proof.  I'm just addressing the OP's request for a quick way to assess the equalities.
