Identify and compare the order of growth: Identify if the following statements are true or false. Prove your assertion using any of the methods shown in the exploration. Draw a rough graph marking the location of $c$ and $n_0,$ if the statement is True. $[$A generic graph would do for this purpose. You don't have to find the values of $c$ and $n_0.$ On the graph you can just write $c$ and $n_0$ without mentioning their values. The idea is that you know how it looks graphically.$].$

a$.n\frac{n+1}{2}$inO$(n^3)$

b$.n\frac{n+1}{2}in(n^2)$

c$.10n-6in(78n+2020)$

d$.n!in(0\mathrm{.}00001n)$