Exercise 2 (2 pts). You know a polynomial-time reduction of 3-SAT to INDEP-SET (see the slides or a dual reduction of 3-SAT to CLIQUE in Theorem 7.32 in the textbook) Apply the reduction described in the course to the following instance of 3-SAT: What is the corresponding instance (G, k) of INDEP-SET? (Draw the graph G.) Exercise 3 (2 pts). The SPARSE SUBGRAPH problem is defined as follows: . Input: (G, p, q> where G is a graph and p, q ? z. .Question: Does G have p vertices such that there are at most q edges between them? Prove that this problem is NP-hard by giving a polynomial-time reduction of INDEP-SET (known to be NP-hard) to SPARSE SUBGRAPH. Hint. Any independent set of size k can be viewed as a "sparse subgraph" consisting of k vertices with no edges between them