Suppose that we have four functions, f, g, F, and G, and that f(n) = O(F(n))...

  

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Suppose that we have four functions, f, g, F, and G, and that f(n) = O(F(n)) and g(n) = O(G(n)). Is it necessarily true that f(n)/ g(n) = O(F(n)/ G(n)) ? If it is true, show that it is true by using the definition of big-Oh. If it is not true, provide counterexample functions f(n), g(n), F(n), and G(n), and explain why the statement is false. Suppose that we have four functions, f, g, F, and G, and that f(n) = O(F(n)) and g(n) = O(G(n)). Is it necessarily true that f(n)/ g(n) = O(F(n)/ G(n)) ? If it is true, show that it is true by using the definition of big-Oh. If it is not true, provide counterexample functions f(n), g(n), F(n), and G(n), and explain why the statement is false.

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