For each type of pattern defined below, determine whether the support measure is monotone, anti-monotone, or non-monotone (i.e., neither monotone nor anti-monotone) with respect to increasing itemset size.
(a) Itemsets that contain both positive and negative items such as {a, b, c, d}. Is the support measure monotone, anti-monotone, or non-monotone when applied to such patterns?
(b) Boolean logical patterns such as {(a ∨ b ∨ c), d, e}, which may contain both disjunctions and conjunctions of items. Is the support measure monotone, anti-monotone, or non-monotone when applied to such patterns?