P2 [20 points] Recall that a vertex cover is a subset of vertices that covers (touches) all the edges in a graph. Formally, given an undirected graph G=(V,E), a vertex cover is a subset VV such that if (i,j)E, then either iV or jV (or both). Then the decision problem, VERTEX-COVER, is to determine whether a graph has a vertex cover of a given size k. It is written in language form as follows: VERTEX-COVER ={G,kG is an undirected graph that has a k-node vertex cover }. A clique, on the other hand, is a subset of vertices that are all directly connected. Formally, given an undirected graph G=(V,E), a clique is a subset VV of vertices, each pair of which is connected by an edge in E. CLIQUE ={G,kG is an undirected graph that has a k-node clique }. Prove that CLIQUE is NP-Complete, by using the fact that VERTEX-COVER is NP-complete