$[35$ pts$]$ Consider the following transactions. Each row corresponds to a transaction where $1$ corresponds

to a presence of an item and $0$ corresponds to an absence$.$

T A B C D

t$11001$

t$20100$

t$31011$

t$41011($a$)[4000-$enrollment only$]$ Let the minimum support threshold be $2.$ Please illustrate the four steps of the

FP$-$tree growth algorithm with the above example.

$($b$)[6000-$enrollment only$]$ An itemset Y is a proper super$-$itemset of X if X $$ Y $.$ An itemset X is said

to be closed if there exists no proper super$-$itemset Y such that Y has the same support count as X$.$

Please illustrate how to use the FP$-$tree growth algorithm to compute all closed itemsets of support

$>=2$ using the above example.