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  3. prove or disprove each of the followings. if f(n

Prove or disprove each of the followings. If f(n) = ?(g(n)), then log2(f(n)) = ?(log2g(n)), where f(n) and g(n) are...

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Advance Math

Prove or disprove each of thefollowings.

  1. If f(n) = ?(g(n)), thenlog2(f(n)) =?(log2g(n)), wheref(n) and g(n) are positivefunctions.

  2. ?(n) + ?(n2) =theta(n).

  3. f(n)g(n) =?(f(n)), where f(n) andg(n) are positive functions.

  4. If f(n) = theta(g(n)), thenf(n) = theta(20 g(n)), wheref(n) and g(n) are positivefunctions.

  5. If there are only finite number of points for whichf(n) > g(n), thenf(n) = O(g(n)), wheref(n) and g(n) are positivefunctions.

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