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 c, . . . , cm. The question is: Does there exist a set X U so that for each i = 1, 2, . . . , m, the cardinality of XnA, is equal to c? We will call this an instance of the Intersection Inference Problem, with input U, {A, and c 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 c, . . . , cm. The question is: Does there exist a set X U so that for each i = 1, 2, . . . , m, the cardinality of XnA, is equal to c? We will call this an instance of the Intersection Inference Problem, with input U, {A, and c Prove that Intersection Inference is NP-complete