(a) (10 points) Prove if f (b) (10 points) Prove if f-0(g), then g-9(f). 1. 0(h) and 1-0(g), then f 0(g). 2. (a) (5 points) Give (Just give names) two sorting algorithms that take average O(n2 time, and two sorting algorithms that take average O(nlogn) time. (b) (10 points) What are the best case and worst case time complexity of the sorting algo- rithms mentioned in the part (a)? Explain why