$(18$pts$)$ In the following, use a direct proof $($by giving values for c and n$0$ in the formal definition of big$-$

O$/\backslash$Omega notation$)$ to prove that:

a$.$ n$2+7$n $+1$ is $\backslash$Omega $($n$2)$

b$.3$n$2+$ n $10$ is O$($n$2)$

c$.$ n$2$ is $\backslash$Omega $($nlogn$)$