Prove the following problem is NP-complete. Consider a store that keeps a database of n customers and the number of each of m products they can buy. The store wants to know if there are at least k customers (ks n) each of whom buy no other products that the other k-1 customers buy. Example: Here, let n 3 and m 4. The table below summarizes the data from the store. Chips 0 Name Fred Barney Wilma Cat Food 0 0 5 Soap Beer 0 0 0 0 The, if k 2, the answer is yes, with either of the sets (Fred, Wilma) or (Barney, Wilma). If k 3, the answer is no. Hint: Reduce the independent set problem to this problem. Prove the following problem is NP-complete. Consider a store that keeps a database of n customers and the number of each of m products they can buy. The store wants to know if there are at least k customers (ks n) each of whom buy no other products that the other k-1 customers buy. Example: Here, let n 3 and m 4. The table below summarizes the data from the store. Chips 0 Name Fred Barney Wilma Cat Food 0 0 5 Soap Beer 0 0 0 0 The, if k 2, the answer is yes, with either of the sets (Fred, Wilma) or (Barney, Wilma). If k 3, the answer is no. Hint: Reduce the independent set problem to this