Assume we perform the following union operations on a disjoint set:

union(A,B), union(C,A), union(D,E), union(F,G), union(C,E), union(B,H), union(I,J), union(G,A), union(I,A).

(a) Draw the resulting up-tree if unions are performed by having the second tree become the child of the first tree.

(b) Draw the resulting up tree if union-by size is used, with ties being broken by using the rule in a).

(c) Show the result of perfoming a find(A) operation on the first tree, using path compression.