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Problem 5. Let f(n) and g(n) be asymptotically nonnegative functions. For each of the following bounds, prove that it does or does not hold: max(f(n),

Problem 5. Let f(n) and g(n) be asymptotically nonnegative functions. For each of the following bounds, prove that it does or does not hold:

max(f(n), g(n)) O(f(n) + g(n))

max(f(n), g(n)) (f(n) + g(n))

max(f(n), g(n)) (f(n) + g(n))

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