Ouestion $1.[30$ pts$]$

Decide if each of the following statements is True or False and provide suitable proof. For a true

statement, you need to identify the values for the constants $c$ and $n_0$ as used in the definitions of Big$-$O

$(O),$ Big$-$Omega $()$ and Big$-$Theta $(),$ then show the corresponding inequalities. For a false

statement, you need to justify$/$prove why finding those constants is impossible.

$[10pts]3n^2+5nlogn$ is $O(n^2)$

$[10pts]2^n+n^2$ is $(2^n)$

$[10$ pts$]n^{2}logn+\sqrt[\phantom{2}]{n}$ is $(n^{2}logn)$