Determine whether the following statements are TRUE or FALSE. Write justification to receive full credit. [6*2.5 = 15 points) i. n integers each of value less than 100 can be sorted in linear time. ii. For hashing an item into a hash table in which collisions are resolved by chaining, the worst-case time is proportional to the load factor of the table. iii. Heapsort, quicksort, and mergesort are all asymptotically optimal, stable comparison based sort algorithms. iv. The following array is a max heap: [10,3,5, 1, 4, 2). In max-heaps, the operations insert, max-heapify, find-max, and find-min all take O(log n) time. vi. There exists a data structure to maintain a dynamic set with operations Insert(x,S), Delete(x,S), and Member?(x,S) that has an expected running time of O(1) per operation. V