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perhaps this question was asked before, but if not give me a hand for it. My question is how to prove that if $W_1$ and $W_2$ be sub-spaces of vector space $V$ with the union of $W_1$ and $W_2$ is also a subspace, then one of the subspace $W_i$ is contained in other ?
Please give me a hint for start. Where should I look here?