Assume that the first listed element is the representative for each set in a disjoint-set. You must show your work. Simply stating the answers will result in 0 points awarded. (20 points) a. Show the data structure of the disjoint set S: {{0, 1, 2}, {3, 5}} as it is being built using both the list and tree representation. b. Consider the following commands applied to the disjoint set S: {{0, 1, 2}, {3, 5}}. MAKE-SET (4) UNION (1,5) UNION (4,5) Show the resulting data structure after applying the commands on the following representations: i. the list representation with weighted union heuristic applied ii. the tree representation with union-by-rank applied c. Given the following tree representation of a disjoint set (see below), use path-compression when executing FIND-SET(9) command using the following procedure. Show the results after each step.