The apriori algorithm makes use of the prior knowledge of subset support properties.1. given a frequent itemset l and a subset s of l, prove that the confidence of the rule s 0 → (l − s 0 ) cannot be more than the confidence of s → (l − s), where s 0 is a subset of s; 2. 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.