$($a$)$ Apply Apriori to the dataset in Q$1-($c$)$ to find frequent itemsets for the minimum support value of $0\mathrm{.}5.$ Show your work of identifying the candidate and frequent $1-$ itemsets, $2-$itemsets, and so on$.[12]$

$($b$)$ Apply k$-$means to cluster the data points with the initial centroids as follows. Show your work of computing the distances $($presented in $2$ decimal places$)$ and centroid updates in each iteration of k$-$means. In case of tie in distance comparison, put the data point to the first cluster. $[13]$

$$ Data points: $(0,1),(5,2),(4,1),(4,2),(2,1),(6,3),$ and $(1,3)$

$$ Initial centroids of C$0$ and C$1$: $(2,1)$ and $(4,3)$