1. k-clique is the following problem. input: a graph G and an integer k query: does G have a clique of size k? a) Define the problem k-independent set. b) Explain why the brute force method for solving k-clique runs in polytime if k is constant but in (2) time when k = n/2. c) Give a polytime answer-preserving transformation T from k-clique to k-independent set (so T takes as input an instance of k-clique and gives as output an instance of k-independent set). Prove that T is polytime. Prove that T is answer-preserving.