Hi I have been given this problem, and I have no idea where to start. So any advice what be great. How to you go about this kind of problem? All the information I was given is:

State whether the following statement is true or false, justify your answer?

Ω(n^5) + o(n^2) + O(logn) = Ω(n^5)

Answer:

`Omega(f(n)) + o(g(n))`

is not really defined well, so I'll try to formally define what you are asking:

if `f(n)`

is in `Omega(n^3)`

, and `g(n)`

is in `o(n^2)`

, is `f(n)+g(n)`

in `Omega(n^3)`

?

The answer to this is yes.

Let's say you have constants `C1, C2`

such that:

```
f(n) >= C1*n^3 (for large enough n)
g(n) < C2*n^2 (for large enough n)
```

Then, `f(n) + g(n) >= C1 * n^3`

(for large enough n)

And you can say `f(n) + g(n)`

is in `Omega(n^3)`

by definition of big Omega.

In fact, you can see from the above, that if `f(n)`

is in `Omega(g(n))`

, then for any (non negative) `h(n)`

, `f(n) + h(n)`

remains in `Omega(g(n))`

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