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Homework Statement
Let U and W be subspaces of a vector space V.
Show that the set
U + W = {v (element symbol) V : v = u + w, where u (element symbol) U and w (element symbol) W}
Is a subspace of V.
Homework Equations

The Attempt at a Solution
I really don't know where to start here? What would I work with? How can I add these vectors to show that their sum is in fact forming a subspace of V? I just don't know where to start?