Q$.7$ Maximal & Closed Itenisets $(20$ points$)$

Given the following transaction data sets $($dark cells indicate presence of an item in a

transaction$)$ and a support threshold of $20\%,$ answer the following questions

a$.$ What is the number of frequent itemsets for each dataset? Which dataset will produce the

most number of frequent itemsets?

b$.$ Which dataset will produce the longest frequent itemset?

c$.$ Which dataset will produce frequent itemsets with highest maximum support?

d$.$ Which dataset will produce frequent itemsets containing items with widely varying support

levels $($i$.$e$.,$ itemsets containing items with mixed support, ranging from $20\%$ to more than

$70\%$

e$.$ What is the number of maximal frequent itemsets for each dataset? Which dataset will

produce the most number of maximal frequent itemsets?

f$.$ What is the number of closed frequent itemsets for each dataset? Which dataset will produce

the most number of closed frequent itemsets?

Name the $3$ data sets from left to right, DS$1,$ DS$2,$ and DS$3$ in your answer.