Counting in Computer Science

$12\mathrm{.}1.$ Let $a_1,$dots,$a_m$ and $b_1,$dots,$b_n$ be two sequences of digits. Consider the following algorithm:

a$.$ How many multiplications will this algorithm conduct?

b$.$ How many times will this algorithm do the larr operation?

$12\mathrm{.}2.$ Explain the difference between $O(n^{2}log(n)),(n^{2}log(n)),$ and $(n^{2}log(n))$ as clearly as you can.

Draw a Venn diagram and give some examples of functions that are in each area of the Venn diagram.

$($BONUS: see if you can include some functions that are not in any of these classes.$)$