$6\mathrm{.}8$ A database has four transactions. Let min$\_$sup $=60\%$ and min $\_$min conf $=80\%.($a$)$ At the granularity of item$\_$category $($e$.$g$.,$ item i could be "Milk"$),$ for the rule template, $$ X in transaction, buys $($X$.,$ item $.\_1)$buys$($X$.,$ item $.\_2)$buys$^$bug$($X$.,$ item $.\_3)[$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,

$$ X in customer, buys $($X$,$ item $\_1)$buys$($X$,$ item $\_2)$buys$($X$,$ item $\_3),$

list the frequent k$-$itemset for the largest k $($but do not print any rules$).$