Consider the following theorem: "If xy = 0, then x = 0 or y = 0." Indicate what, if anything, is wrong with each of the following "proofs."
(a) Suppose xy = 0 and x ≠ 0. Then dividing both sides of the first equation by x we have y = 0. Thus if xy = 0, then x = 0 or y = 0.
(b) There are two cases to consider. First suppose that x = 0. Then x · y = 0 · y = 0. Similarly, suppose that y = 0. Then x · y = x · 0 = 0. In either case, x · y = 0. Thus if xy = 0, then x = 0 or y = 0.
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