Hello,
I am stuck with this problem.
prove that the union of two subspaces of the vector space is a subspace of if and only if one of the subspaces is contained in the other.
Thanks in advance for your help.
Yes, I think I get that part. Is it right like this?
If and are subspaces of and .
Then .
So is a subspace of
But how would you the other way. Assuming first that the union of two subspaces, say and , of the vector space . Then how do you prove that one of them is contained in the other?