Prove parts (a), (c), and (e) of Theorem 1 analytically. (a) u + v = v +

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Prove parts (a), (c), and (e) of Theorem 1 analytically.
(a) u + v = v + u
(c) (u + v) + w = u + (v + w)
(e) k(lu) = (kl)u
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