Isomorphism between 2 quotient spaces Let $M,N$be linear subspaces $L$ then how can we prove that the following map
 $$(M+N)/N\to M/M\cap N$$ defined by $$m+n+N\mapsto m+M\cap N$$ is surjective?
Originally, I need to prove that this map is bijection but I have already proven that this map is injective and well defined,but having hard time to prove surjectivity,please help.

Define $T: M \to (M+N)/N$ by 
          $m \mapsto m+N$. 
Show that it is linear and onto. 
Check the $\ker T$  and is $M\cap N$ 
by the first isomorphism theorem $f:M/(M\cap N) \to (M+N)/N$ is an isomorphism.
