Consider the function   f(n) = 2n if n is even f(n) = 3n^2 if n is odd  From the definitions: i) Prove or disprove that f(n) is O( n^2) (`Big-Oh of n squared’). ii) Prove or disprove that f(n) is Ω( n^2) (`Big-Omega of n squared’). iii) Prove or disprove that f(n) is o( n2^2) (`little-oh of n squared’)  I have proven (i) and disproven (iii), I am having trouble with (ii), becuase if i choose c = 1 and n0 = 1, i get this inequality 4 >= 4 which is true, but for any other value of n it is false, but is this correct since it's only there exists c and n0 such that f(n) >= c g(n) or do other n values, for example n0 = 2, 3 ,4 , need to be true as well for it to be proven? Thank you very much

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