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Prove f(n)=O(g(n)) implies g(n)=Omega(f(n))
easy
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Prove f(n)=O(g(n))
implies g(n)=Omega(f(n))
Analyze the prove f(n)=o(g(n)) implies g(n)=omega(f(n)).
Examples
Example 1
Input:
"proof_case_1"
Output:
true
Example 2
Input:
"proof_case_2"
Output:
true
Hints
Hint 1
Recall the definitions of **little-o** and **omega** notations. How do they relate to the inequalities involving limits?
Hint 2
Use the formal definition of **f(n) = o(g(n))** to derive a relationship between f(n) and g(n) as n approaches infinity.
Hint 3
Prove the contrapositive: Assume **g(n) ≠ ω(f(n))**, then show that this contradicts the given **f(n) = o(g(n))** by analyzing the limit behavior.
Prove f(n)=O(g(n)) implies g(n)=Omega(f(n))
Analyze the prove f(n)=o(g(n)) implies g(n)=omega(f(n)).