Consider the following transactional data from a computer shop.

Table $3\mathrm{.}1$

Assume that the minimum support is $50\%$ and confidence is $80\%.$

$($a$)$ Find all the frequent item sets. In your answer, show the candidate item sets obtained at each step of the pruning stage and list down all the frequent item sets.

$($b$)$ Generate the Apriori rule$($s$)$ for frequent item set L$3.$ In your answer, show the working steps on how you obtain the rules and list down the finalised rules.

$($c$)$ Determine support and lift for the identified rule$($s$)$ in Q$3($b$).$

$($d$)$ Identify the least popular item that you observe from the Apriori rule$($s$)$ in Q$3($b$).$

$($e$)$ Based on your observations in Q$3($d$),$ provide TWO $(2)$ suggestions to the retailer to improve the sales.