I know the question sounds easy but I am still confused with that... Say
- $$A = 7^n; B=7^{n+log(3n)}$$
- $$C = 2^{7n}; D = 2^{n}$$ Then, I believe A=O(B) and C=Ω(D) right? However, I am struggling with another exceptional case. Here is the problem. Okay, I just apply the definitions of big O notation but I see there are several exceptional cases. Say if $$X=3^n$$ and $$Y=2^n$$, then X is not a member of the Big O family of Y. This is because we cannot find a constant k to satisfy the condition stated in the definition of Big O family. Thanks!