We start by defining the Independent Set problem. Given a graph G = (V, E), we say a set of nodes S V is independent if no two nodes in S are joined by an edge. The Independent Set problem, which e denote IS, is the following. Given G, find an independent set that is as large as possible. State as a decision problem, IS answers the question, does three exist a set S G such that |S| greaterthanorequalto k? Then set k as large as possible. For this problem, you may take as given that IS NP-complete. A store trying to analyze the behavior of its customers will often maintain a table A where the rows of the table correspond to the customers and the conduits (or fields) correspond to products the store sells. The entry A(i, j) specifies the quantity of product j that has been purchased by customer For example, Table?? Show one such table. One thing that a store might want to do with this data is the following. Let's say that a subject S of the customers is diverse if no two of the customers in S have ever bought the same product (i.e., for each product, at most one of the customers in S has ever bought it). A diverse set of customers can be useful, for example, as a target pool for market research. We can now define the Diverse Subset problem (DS) as follows: Given an m times n array A as defined above and a number k lessthanorequalto m, is there a subset of at least k customers that is diverse