Hi,

problem:Suppose that is a subspace of a vector space . Prove that a subset of is an equivalence class modulo if and only if it is a coset of

attempt:

Let be a subset of .

1st direction: If is a coset of , then it is an equivalence class modulo .

.

Now, I don't really know how to go from N beeing a coset of M to it beeing an equivalence class modulo M. Any help is greatly appreciated!

Thanks.