For each of the following measures, determine whether it is monotone, anti-monotone, or non-monotone (i.e., neither monotone nor anti-monotone).
Example: Support, s = σ(X)/|T| is anti-monotone because s(X) ‰¥ s(Y) whenever X Š‚ Y.
(a) A characteristic rule is a rule of the form {p} †’ {q1, q2, ... , qn}, where the rule antecedent contains only a single item. An itemset of size k can produce up to k characteristic rules. Let ζ be the minimum confidence of all characteristic rules generated from a given itemset:

Is ζ monotone, anti-monotone, or non-monotone?
(b) A discriminant rule is a rule of the form {p1, p2, ... , pn} †’ {q}, where the rule consequent contains only a single item. An itemset of size k can produce up to k discriminant rules. Let η be the minimum confidence of all discriminant rules generated from a given itemset:

Is η monotone, anti-monotone, or non-monotone?
(c) Repeat the analysis in parts (a) and (b) by replacing the min function with a max function.

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