Discrete math

1. Let a₁,...,a_m and b₁,...,b_n be two sequences of digits. Consider the following algorithm: s 0 for i {1, ..., m} do: for j {1, ..., n} do: s s + a_i b_j a) How many multiplications will this algorithm conduct?

b) How many times will this algorithm do the operation?

2. Explain the difference between O(n²log(n)), (n²log(n)), and (n²log(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.)