Is the Operation Linear and Bijective?

[schw]

Could anyone help me solve this problem?

Let A,B be two subspace of V, a \in A, b \in B. Show that the following operation is linear and bijective:

(A + B)/B → A/(A \cap B): a + b + B → a + A \cap B

I really couldn't understand how the oparation itself works, i.e, what F(v) really is in this problem.

 

[mathwonk]

write v as a+b, then F(v) = a. now chck this is well defined, i.e. if a+b ≈ a'+b' modb, then a ≈ a' mod (AmeetB).

 

[schw]

I just have to ignore the sets that are in the operation? (v = a + b + B)

edited:
Just realized the definition of quocient space. Tahnks for helping