3. (Exercise 8.16 from Kleinberg & Tardos) (7 points) Consider the problem of reasoning about the identity of a set from the size of its intersections with other sets. You are given a finite set U of size n, and a collection Ai,-. ,Am of subsets of U. You are also given numbers ,cm The question is: Does there exist a set X C U so that for each i-1,2,..., m, the -U80 u Cne cardinality of XnA, is equal to c? We will call this an instance of the Intersection Inference Problem, with input U, A, and ). Prove that Intersection Inference is NP-complete. 3. (Exercise 8.16 from Kleinberg & Tardos) (7 points) Consider the problem of reasoning about the identity of a set from the size of its intersections with other sets. You are given a finite set U of size n, and a collection Ai,-. ,Am of subsets of U. You are also given numbers ,cm The question is: Does there exist a set X C U so that for each i-1,2,..., m, the -U80 u Cne cardinality of XnA, is equal to c? We will call this an instance of the Intersection Inference Problem, with input U, A, and ). Prove that Intersection Inference is NP-complete