Castings are produced weighing either (1,5,10), or (20 mathrm{~kg}). Let (A, B), and (C) be the events

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Castings are produced weighing either \(1,5,10\), or \(20 \mathrm{~kg}\). Let \(A, B\), and \(C\) be the events that a casting weighs 1 or \(5 \mathrm{~kg}\), exactly \(10 \mathrm{~kg}\), and at least \(10 \mathrm{~kg}\), respectively. Characterize verbally the events \(A \cap B, A \cup B, A \cap \bar{C}\), and \((\bar{A} \cup \bar{B}) \cap C\).

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