Let $P,Q,R$ be subspaces of a vector space $V$ such that $V=P \cup Q \cup R$ , then is it true that one of $P,Q,R$ must be equal to $V$ ? I know the result about subspaces that tells that if for subspaces $A,B$ , $A \cup B$ is also a subspace then $A \subseteq B$ or $B \subseteq A$ , but for this three union case I cannot make any headway , Please help . Thanks in advance
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here is a similar question.Look at it. – A.B. Feb 25 '15 at 12:38
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@SaunDev See the solution given here – Ben Grossmann Feb 25 '15 at 12:48