23 (15 points) This question is related to disjoint set operations. Assume that we are using union by rank and find with path compression. Suppose that you are given a disjoint set structure described by the following array. The following three sub-questions all refer to this disjoint set (not the disjoint set you obtained after doing some operations). (a) On the answer sheet, show the result after applying union (8, 12) to the disjoint set at the start of this question. (b) On the answer sheet, show the result, after applying union (16,6) to the disjoint set at the start of this question. (c) On the answer sheet, show the result after applying find-set(15), find-set (8) to the disjoint set at the start of this question. 23: Read the instructions for question Q3 in the assignment document. For each of the three sub-questions, write your answer to the question in the given space. (a): After performing union (8,12), we have A[1]= A[4]= A[9]= A[15]= A[16]= (b): After performing union (16,6), we have A[1]= A[6]= A[9]= A[15]= A[16]= (c): After performing find-set(15) and find-set(8), we have A[1]- A[7]= A[B]= A[9]= A[16]=