Item 1 is in basket J if and only if I divides J evenly. For example basket is 24 is the set of items {1,2,3,4,6,8,12,24}. Describe all the association rules that have 100% confidence.

• Items = { 1, 2 ….. 100}

• Baskets = {B1, B2, …. B100}

For eg B24 = {1, 2, 3, 4, 6, 8, 12, 24}

• Support (A) = occurrence of A in every basket.

• Confidence (A-B) = $\frac{support (AUB)}{support A}$

• In above example the rules can be constructed as:

1 – {1}

2 – {1,2}

3 – {1,3}

4 – {1,2,4}

5 – {1,5}

And so on.

• If we observer item 1 is only occurring in every basket.

• To have 100% confidence the item has to appear in every basket. Which is item 1 only.

• So any rule fr eg. {3,5} – 1 has 100% confidence.