The Apriori algorithm makes use of the prior knowledge of subset support properties. Given a frequent itemset l and a subset s of l, prove that the confidence of the rule s' rightarrow (l - s') cannot be more than the confidence of s rightarrow (l - s), where s' is a subset of s; A partitioning variation of Apriori subdivides the transactions of a database D into n nonoverlapping partitions. Prove that any itemset that is frequent in D must be frequent in at least one partition of D