NOTE: Unless otherwise specified, in this assignment, we use sup(A) to denote the absolute support of an itemset A and s(A) to denote the relative support of an itemset A. Problem 1. True or False (24 points) Please justify your answers with at most 3 sentences ( 1 point for true or false and 2 points for the justification). (1) (3 points) Suppose two association rules are derived from the same frequent pattern, they (i.e., the two association rules) must share the same support and confidence. (2) (3 points) Pattern A is a max-pattern if A is frequent and there has no super-pattern BA that is frequent. Besides, max-pattern is a lossless compression of frequent patterns. (3) (3 points) Given two itemsets A and B, the range of Kulczynski(A,B) measure of A and B is (0,1), i.e., Kulczynski (A,B)(0,1). (4) (3 points) In Apriori Algorithm, if there is any itemset which is infrequent, its superset can not be generated. (5) (3 points) When a given database to be mined is extremely large and FP-tree cannot fit into the memory, it is impossible to mine the database using FPGrowth algorithm. [Hint: you may refer to textbook for answer.] (6) (3 points) Given two frequent itemsets A and B, we denote s(A),s(B) and s(AB) as the relative support of A, the relative support of B and the relative support of AB, respectively. If s(AB)s(A)s(B), it implies itemsets A and B rarely occur together. (7) (3 points) Let A be an itemset and V be another bigger itemset. Is AV antimonotone? If true, please explain the reason. Otherwise, please provide an counterexample. (8) (3 points) Let V={a,b,c,d,e} be the set of all items, A={a,b,c} and B={a,b,c,e} be two itemsets. Is AB monotone? If true, please explain the reason. Otherwise, please provide an counterexample