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. 

We have $A\setminus B=A\setminus (B\cap A)$ and $A\setminus C=A\setminus (C\cap A)$. Given $B\subset C\subset A$.
$$\begin{align}A\setminus B&=A\setminus C\\\implies A\setminus (B\cap A)&=A\setminus (C\cap A)\\\implies B\cap A&=C\cap A\\\implies B&=C{[\text {using} B\subset C\subset A]}.\end{align}$$
