Consider the data set shown in Table 7.8. The first attribute is continuous, while the remaining two attributes are asymmetric binary. A rule is considered to be strong if its support exceeds 15% and its confidence exceeds 60%. The data given in Table 7.8 supports the following two strong rules:
(i) {(1 ‰¤ A ‰¤ 2),B = 1} †’ {C = 1}
(ii) {(5 ‰¤ A ‰¤ 8),B = 1} †’ {C = 1}
Table 7.8. Data set for Exercise 3.

(a) Compute the support and confidence for both rules.
(b) To find the rules using the traditional Apriori algorithm, we need to discretize the continuous attribute A. Suppose we apply the equal width binning approach to discretize the data, with bin-width = 2, 3, 4. For each bin-width, state whether the above two rules are discovered by the Apriori algorithm. (The rules may not be in the same exact form as before because it may contain wider or narrower intervals for A.) For each rule that corresponds to one of the above two rules, compute its support and confidence.
(c) Comment on the effectiveness of using the equal width approach for classifying the above data set. Is there a bin-width that allows you to find both rules satisfactorily? If not, what alternative approach can you take to ensure that you will find both rules?

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