I am struggling with this question from Halmos's text, please ignore the imperative language.
"Suppose that $L, M$ and $N$ are subspaces of a vector space. Show that the equation
$$L \cap (M + N) = (L \cap M) + (L \cap N)$$
is not necessarily true.
Since each of these subspaces has origin in them, clearly there intersections could not be empty. I wasn't able to formulate an example where this result did n't hold. Any help would be highly appreciated.