a) Describe the difference between the and O notation b) Assume the running time of a function is T(n)-n log n. Which of the following are true and which are false T(n) = 0(n) T(n) = 0(n log n), T(n) = 0(), T(n)-O (n), T(n)- (n log n) c) Is 2n+ O(2) true? What about 22 O(2)? STUDY PROBLEM 2 Show which case is true fin)-O(g(n)), fin) following function pairs. Justify your answer 0(g(n)), or fin) 6(g(n)) for each of the (a) f(n)-log n; g(n) log n +5 (b) f(n)-n log n+ n; g(n) -log n (c) f(n)- 10; g(n) -log 10 (d) f(n) - vn; g(n) n+log n STUDY PROBLEM 3 Show that: b) n3-3n2-n+ (n3) In both cases, you need to show that there exist constants no, ci and c2 as specified in -notation definition