Recall that CLIQUE E NP, where CLIQUE is defined as: CLIQUE-{(G, k) : G (V,E) has a clique of size k). (A clique is a subset C C V of vertices such that for all u, v E C, (u, v) E E.) (a) Prove that CLIQUE is NP-complete. Consider the following variants of CLIQUE. For each language, state (with proof) whether it is in P or it is NP-complete. (b) HALF-CLIQUE = {(G): |v| = 2n, and G has a clique of size-n) (c) 376-CLIQUE -[G): G has a clique of size 3761