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Let $ W, W_1, W_2,W_3,\ldots,W_n$ be $n+1$ subspaces of a vector space $V$. Show that if $W \subset W_1 \cup W_2 \cup W_3 \cup \cdots\cup W_n$, then $W$ is contained in one of $W_1, W_2,W_3,\ldots,W_n$.

I am lost as to how to go about proving this. Any help would be much appreciated.

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    As stated, it's trivially true: $W$ is always contained in $W$. – 2017-01-29
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    Didn't see that :D – 2017-01-29
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    That was a typo. Sorry – 2017-01-29
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    Over a finite field it's not true. – 2017-01-29
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    @Litho can you provide a counterexample? – 2017-01-29
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    Vector space over what? If over an arbitrary field, then the result is false: if $F$ is the two element field, then $F^2$ is the (finite) union of its proper subspaces. – 2017-01-29
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    @AlexMathers Any vector space of finite dimension >1 over a finite field has a finite number of elements, so it can be represented as a finite union of its 1-dimensional proper subspaces. – 2017-01-29

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