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 $2^k+1(k+1{)}^2$

What should $be$ proven $in$ the inductive step?

$a.$ For $n=4,2^n{n}^2$

$b.2^k{k}^2$

$c.$ For every $k>4,if{2}^k{k}^2$ then $2^k+1(k+1{)}^2$