Suppose A and B are non-empty sets of real mumbers that are both bounded above. (a) Prove that, if A C B, then sup A < sup B. (b) Prove that sup AUB = max{sup A, sup B}. (c) Prove that, if ANB + Ø, then sup AnB < min{sup A, sup B}. Give an example to show that equality need not hold.

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