A database has four transactions. Let min_sup \(^{\text {4 }}=60 \%\) and min_conf \(^{\text {s }}=80 \%\).

a. At the granularity of item_category (e.g., item \({ }_{i}\) could be "Milk"), for the rule template,
\[
\forall X \in \text { transaction, buys }\left(X, \text { item }_{1}ight) \wedge \operatorname{buys}\left(X, \text { item }_{2}ight) \Rightarrow \text { buys }\left(X, \text { item }_{3}ight) \quad[s, c],
\]
list the frequent \(k\)-itemset for the largest \(k\), and all the strong association rules (with their support \(s\) and confidence \(c\) ) containing the frequent \(k\)-itemset for the largest \(k\).
b. At the granularity of brand-item_category (e.g., item \({ }_{i}\) could be "Sunset-Milk"), for the rule template,
\[
\forall X \in \text { customer, } \operatorname{buys}\left(X, \text { item }_{1}ight) \wedge \operatorname{buys}\left(X, \text { item }_{2}ight) \Rightarrow \text { buys }\left(X, \text { item }_{3}ight),
\]
list the frequent \(k\)-itemset for the largest \(k\) (but do not print any rules).

T100 cust_ID TID items_bought (in the form of brand-item_category) 01 King's-Crab, Sunset-Milk, Dairyland-Cheese, Best-Bread} T200 (Best-Cheese, Dairyland-Milk, Goldenfarm-Apple, Tasty-Pie, Wonder-Bread} T300 (Westcoast-Apple, Dairyland-Milk, Wonder-Bread, Tasty-Pie} 02 01 03 T400 (Wonder-Bread, Sunset-Milk, Dairyland-Cheese}