How to prove if $\bigcup_{k=1}^{n}V_{k}$ is a subspace over $\mathbb{C}$ then $\bigcup_{k=1}^{n}V_{k}=V_{j}$ for some j?
For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$?