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

Prove or disprove each of the followings.

If f(n) = ω(g(n)), then log₂(f(n)) = ω(log₂g(n)), where f(n) and g(n) are positive functions.
ω(n) + ω(n²) = theta(n).
f(n)g(n) = ω(f(n)), where f(n) and g(n) are positive functions.
If f(n) = theta(g(n)), then f(n) = theta(20 g(n)), where f(n) and g(n) are positive functions.
If there are only finite number of points for which f(n) > g(n), then f(n) = O(g(n)), where f(n) and g(n) are positive functions.

Expert Solution

Colby Messinger answered 2 years ago

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Question

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

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