Comparing asymptotic notations I have a problem P that is said to be O(n^7) in the worst case.
I'm asked to agree or not if it is solvable in O(n^9) time. And also I'm asked to agree or not if P cannot be solved faster than Ω(n^7) in the worst case.

My answer for the first question is that if P is bounded by O(n^7) it is also solvable in O(n^9).

And for the second question: Ω(n^7) means that the running time cannot be less than n^7, but we already know that P is bounded by O(n^7) in the worst case and it is not proven that it can't be solved faster, so I think this statement is false. 

So my questions are: how do I prove the answer for the first question and how do I express my second answer in terms of functions? 
I've seen a lot of info about asymptotic notations, but I couldn't find any info that could enlighten me how to answer the questions I am asked.

Thanks.
If P is solvable in $O(n^7)$, that means that P is solvable in $C \cdot n^7$ time, for some constant $C&gt;0$ and large enough $n$. Since $C \cdot n^7 &lt; C \cdot n^9$ for large enough $n$, that implies that P is solvable in $O(n^9)$.

P is bounded by O($n^7$) in the worst case, but it does not imply that in the best case cannot run in constant time, for instance. Thus, P is not greater than $C \cdot n^7$ for large enough $n$, so it is not $\Omega(n^7)$.