Affine Subspace Confusion I'm having some trouble deciphering the wording of a problem.
I'm given $V$ a vector space over a field $\mathbb{F}$.  Letting $v_1$ and $v_2$ be distinct elements of $V$, define the set $L\subseteq V$: $L=\{rv_1+sv_2 | r,s\in \mathbb{F}, r+s=1\}$.
It's the next part where I can't figure out what they mean.
"Let $X$ be a non-empty subset of $V$ which contains all lines through two distinct elements of $X$."
No idea what this set $X$ is.  Once I figure that out, I'm supposed to show that it's a coset of some subspace of $V$.  I'm hoping this part will become clearer once I know what $X$ is...

By definition the set $L$ in your question consists of all the points on a line. So you may think of $L$ as a line (or the line that passes through the two points $v_1$ and $v_2$).
Hence if you are considering the two points ($v_1$, $v_2$) giving you the line $L$, then a subset $X$ containing all lines (the one line) through the two points, is a subset $X$ containing $L$: $L \subseteq X$.
Note: There might be a bit confusion here since by saying "$X$ contains all lines..." you might be understood as saying that the elements of $X$ are lines. But that would mean that $X$ is not a subset of $V$, so I assumed that you by "$X$ contains all lines..." mean that $X$ contains all the points on the lines (all the points that make up the lines).
