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Calculus and Beyond Homework Help
The union of three subspaces of V is a subspace of V
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[QUOTE="SC0, post: 6086297, member: 438020"] Yeah, I apologize for the mess. I found it very difficult to organize my thoughts regarding this question and I ended up writing it in an unclear way. What I'm trying to prove is this: (Union of three subspaces of V is a subspace of V) ##\Rightarrow## (One of the subspaces contains the other two) As regarding the "previous condition" and every usage of the word "condition" in my post, it refers to this: Let it be that for all the subsets: [B]x[/B]+[B]y[/B]∈U[SUB]x[/SUB] ##\vee## [B]x[/B]+[B]y[/B]∈U[SUB]y[/SUB] where, [B]x[/B],[B]y[/B] ∈ {a,b,c} and [B]x[/B]≠[B]y[/B]. What I mean by that is that if x ∈ U[SUB]a[/SUB] and y ∈ U[SUB]b[/SUB] then x+y belongs to either one of them, as opposed to some other subset. Please let me know wherever clarification is needed, and thanks for the help, this problem has been bugging me for a while now. [/QUOTE]
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The union of three subspaces of V is a subspace of V
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