Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$. Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
The forward implication is easy to prove but i got stuck at the backward implication, i.e. $(U\setminus B)\subseteq(U\setminus A)\Rightarrow A\subseteq B$. Can someone help me out with it? Thank you.

Hint: apply the forward implication to $A'=U\setminus B$ and $B'=U\setminus A$.
