Suppose that $S_1$ and $S_2$ are nonzero subspaces, with $S_1$ contained inside $S_2$, and suppose that $dim(S_2) = 4$

? 1 2 3 4 1 or 2 1, 2, or 3 1, 2, 3, or 4  1. What are the possible dimensions of $S_1$?

? 1 2 3 4 1 or 2 1, 2, or 3 1, 2, 3, or 4  2. If $\ S_1 \ne S_2$, then what are the possible dimensions of $S_1$ ?