$2.$ Consider a proof of the following fact:

For all, n $>=4,2^$n $>=$ n$^2$

$($provide brief explanation for your answer$)$

What should be proven in the base case?

a$.$ For n $=1,2^$n $>=$ n$^2$

b$.$ For n $=4,2^$n $>=$ n$^2$

c$.2^$k $>=$ k$^2$

d$.$ For every k $>4,$ if $2^$k $>=$ k$^2$ then $2^$k$+1>=($k$+1)^2$