4. Let G be a graph. An independent set of G is a set of nodes in G such that no two nodes in the set are joined by an edge. Define I (G, k G has an independent set with k elements J. Show that I is NP-complete as follows: Show that is NP. For a graph G, define G to the complementary graph of G; that is, two nodes u and u arejoined by an edge in?if and only if u and u are not j?ned by an edge in G. Show that for all positive integers k, G has a clique with k elements if and only if G has an independent set with k elements. Using the above result, show that CLIQUE is polynomial-time map- ping reducible to