To prove or disprove an union of two subspaces is a subspace if and only if an intersection of them within them

Question

Let $U$ and $V$ be subspaces of a vector space $W$.

Prove or disprove that $U \cup V$ is a subspace of $W$ if and only if

$U \cap V \in \{U, V\}$

I am not sure what "$U \cap V \in \{U, V\}$" exactly means.

By the way, how to type Latex in here?

Answer 1

$$U\cap V\in\{U,V\}$$ gives $$U\cap V\in\{U,V\}$$which means: $$U \cap V=U\quad\text{or}\quad U \cap V=V.$$