Answer all parts of the question for a like!

$($b$)$ Suppose the support of $\{A,B\}$ is the same as the support of $\{B,C\},$

which one of the following statements are true:

i$.$ All transactions that contain $\{A.B\}$ also contain $\{B.C\}.$

ii$.$ The confidence of the rule $\{A,B\}\{C\}$ is $100\%.$

iii. The support of $\{A,B,D\}$ is the same as the support of $\{B,C,D\}.$

iv$.\{A,B,D\}$ is not a closed itemset.