(a) Recall that the INDEPENDENT-SET problem is NP-complete. Prove that the following variant of the INDEPENDENT-SET problem, namely the 3-INDEPENDENT-SET problem, has a polynomial time algorithm: Given an undirected graph G = (V, E), determine if there is a set S of three vertices {v_1, v_2, v_3} such that no two vertices in S are joined by an edge. (b) Let d be any positive integer. An undirected graph G = (V, E) is said to be d-regular if every vertex v elementof V has degree d, (i.e., there are exactly d edges (v, x) for some vertex x in G). Define the 2-Regular Subgraph problem as follows: Given an undirected graph G = (V, E), determine whether G has a subgraph G' such that G" (i) is connected, (ii) covers all the vertices, and (iii) is 2- regular Prove that the 2-Regular Subgraph problem is NP-complete