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 check quickly, you can use the boolean logic, i.e. replacing the set $A$ with statement $a = (x \in A)$. Thus you get (using $A - B = A \cap B^C \Leftrightarrow  a*\neg b$ ):
$$a * \neg (b+c) = (b*\neg c)*\neg a$$
$$a * \neg b * \neg c = (b*\neg c)*\neg a$$
this should be equal for all $a,b,c$, but for $(1,0,0)$ we have
$$1 = 1*\neg 0*\neg 0 = (0*\neg 0) *\neg 1 = 0$$
which is contradiction.
