Suppose there are $120$ items, numbered $1$ to $120,$ and also $120$ baskets, also numbered $1$ to Item $i$ is in basket $b$ if and only if i divides $b$ with no remainder. Thus, item $1$ is in all the

baskets, item $2$ is in all sixty of the even$-$numbered baskets, and so on$.$ Basket $12$ consists of

items $\{1,2,3,4,6,12\},$ since these are all the integers that divide $12.$ Answer the following questions:

$(1)$ If the support threshold is $6,$ which items are frequent?

$(2)$ What is the confidence of the following association rules?

a$)\{3,4\}5$

b$)\{2,3,6\}7$

$(3)$ Apply the A$-$Priori Algorithm with support threshold $6$ to compute:

a$)$ the candidate itemsets of size $1$ and truly frequent itemsets of size $1.$

b$)$ the candidate itemsets of size $6$ and truly frequent itemsets of size $6.$