5. Are the following true or false, and prove your answers: (a) If A is compact and B is bounded, then An B is compact. (b) If A is compact and B is closed, then An B is compact. (c) If A is compact and B is bounded, then AUB is compact. (d) If A is compact and B is closed, then AUB is compact.

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A: We use the definition of modulus function to solve this problem.

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A: Set theory

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A: Note we consider A = A p Let A p⊂B, where B is bounded.

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