Please write a full answer, and give a good explanation

4 Below are statements that are either true or false. For each statement say whether it is true or false and justify your answer in a few words a) The Radix sort algorithm in the textbook uses Counting sort to sort individual digits. We could swap Counting sort out for another sorting algorithm, e.g. Quicksort, and Radix sort b) We only need O(1) rotations in the worst case when inserting into a red-black tree with n c) If all the edge weights of a graph G are multiplied by a positive constant c, then the minimum d) If the graph G has edges with negative weights, then Dijkstra's algorithm for shortest path can e) Assume the problem TAS is in the complexity class NP and let SAT be the NP-complete would still work correctly. nodes spanning tree of G is unchanged get into an infinite loop on G problem Satisfiability. If we prove that TAS P SAT then TAS is also NP-complete