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. 

see here, for what "∖" means. for other part: 
you have $B \subset  C$. I prove $C \subset B$  
Let $x\in C$. so $$ x\in A\ and\   x\notin (A\setminus C)$$ which means $$x\in A\ and\   x\notin (A\setminus B)$$ therefore $x\in B$
