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spanning sets

How would I prove that

Sp (S U T) = Sp(S) U Sp(T)

where S and T are subsets of V

so far I have

S=(va1, va2...van)

T=(vb1, vb2...vbn)

S U T = (va1, va2...van, vb1, vb2...vbn)

Sp(S U T) = (t1va1, t2va2...tnvan,fvb1, fvb2... fvbn)

Sp (U) = (t1va1, t2va2...tnvan)

Sp T = (tnvan,fvb1, fvb2... fvbn)

thus Sp (S U T) = Sp(S) U Sp (T)

where ti, fi are real numbers and vai and vbi are vectors in V
Is this correct?

Is it also true that Sp (S U T) = Sp (S) + Sp(T)?

not really sure how to go about this