I have trouble answering the following question: 

If $V$ and $W$ are subspaces of $\mathbb{R}^n$, is the union of $V$ and $W$ necessarily a subspace of $\mathbb{R}^n$? 

Given $V$ and $W$ are subspaces, the zero vector must be present, but I have a hard time understanding how to "proof" closed under multiplication and addition. 

Thank you!