Vector space/Union of linear subspaces/Exercise

Let ${}K$ be a field, and let ${}V$ be a ${}K$-vector space. Let ${}U,W\subseteq V$ be subspaces of ${}V$. Prove that the union ${}U\cup W$ is a subspace of ${}V$ if and only if

${}U\subseteq W$ or ${}W\subseteq U$.

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