Question 4: Give a data structure that has keys that are positive integers. The data structure should support:

(a) Insert(S, x)

(b) Delete(S, x)

(c) Search(S, x)

(d) Is_prime(S,x) In this operation we find teh vertex x. Consider the tree Tx rooted by x. Answer yes if there is a prime number in Tx and answer no otherwise. Assume that you are given an algorithm that given a positive interger x, tells you in O(1) time if x is prime.