Does $A\setminus B = A\setminus C$ imply $B=C$? Let $A, B, C$ be sets with $B \subset  C$ and $C \subset  A$. Does $A\setminus B = A\setminus C$ imply $B=C$?
I am not sure what the "\" means, so I don't know how to solve this. 

Yes it does, since, if $B\subset A$, then $A\setminus (A\setminus B)=B$. So $A\setminus B = A\setminus C$ implies $A\setminus (A\setminus B) = A\setminus (A\setminus C)$, i.e.  $\,\,B=C$.
