Vector subspace equality proof/disproof. Given $R,S,T$ are subspaces of vector space $V$, and $R+S=R+T$, does it follow $S=T$?
Please don't give a full proof, but some general help would be much appreciated. I get the basic idea that to show $S=T$ would be to show them to be subsets of one another. Not sure how to do this in a concrete way though.

No. Think about the following example. V is the plane, R is a line which passes the origin, S, T are different lines which also pass the origin.
