# 100 items 100 baskets divisor association analysis problem

I have the following exercise question:

Suppose there are 100 items, numbered 1 to 100, and also 100 baskets, also numbered 1 to 100. 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 fifty of the even-numbered baskets, etc. for example Basket 12 consists of items {1, 2, 3, 4, 6, 12}

Given this, I'm trying to solve the following 3 questions:

(a) If the support threshold is 5, which items are frequent?

(b) what is the confidence of the following association rules?

(1) {5, 7} → 2.

(2) {2, 3, 4}→ 5.

which way I should be approaching these types of questions?

• Isn't this best suited for Mathematics SE or maybe Cross-validated SE ? I fail to see how this is related to Data Science, this is rather related to pure probability/set math and how it fit data-mining itself. Note: Although this is an important concept for the tags referred this is not applied but rather pure math. – Pedro Henrique Monforte Apr 9 at 18:29

a) The items that are frequent are $$\{1,2,3,4,5,\dots,20\}$$ because these all appear in at least 5 baskets.

b)

(1) $$\{5, 7\} → 2$$. Then $$Confidence=\frac{1}{2}$$

hence 5 and 7 will appear together in basket no. 35 and 70 and 2 will appear along with 7 and 5 in basket no. 70 so:

$$Confidence = \frac{support(\{5,7\}\cup\{2\})}{support(\{5,7\})}= \frac{1}{2}$$

(2) $$\{2, 3, 4\}→ 5$$. Then $$Confidence=\frac{1}{8}$$

$$\{2,3,4\}$$ appear in baskets having basket number multiple of 12 ($$LCM\{2,3,4\}$$) i.e in basket no $$\{12,24,...,60,.....,96\}$$ and $$\{2,3,4,5\}$$ appear together only in basket no 60.

$$→ Confidence=\frac{1}{8}$$