Assume an itemset X = {i1,...,ik}{i1....,ik} with k items. Consider the k rules formed by putting one item on the left-hand side of the rule, and all the remaining items on the right-hand side. Let a(X)a(X) be the minimum confidence of all these rules: a(X)=min[c({i}{i2,...,ik}),...,c({ix}{i 1,...,ik-1})]a(x)=min[c({1}-{i2....,ik}},... c{{ik){i1,...,ik-1})], where c denotes the confidence of a rule. Is the measure a a monotone, anti- monotone or non-monotone? Explain why. Hint: Use the definition of confidence and simplify the expression for aa. 1 (c) Similarly as in (b), but now we replace the minimum by the maximum. Let B(X)B(X) be the maximum confidence of all these rules: B(X)=max(c({i} {i2....,ik})....,c({ix) - {11...,ik-1))B(X)=max(c({11}-{i2....,ik})... ..c[{ik}-{i1....,ik-1}}} Is the measure BB monotone, anti-monotone or non-monotone? Explain why. Assume an itemset X = {i1,...,ik}{i1....,ik} with k items. Consider the k rules formed by putting one item on the left-hand side of the rule, and all the remaining items on the right-hand side. Let a(X)a(X) be the minimum confidence of all these rules: a(X)=min[c({i}{i2,...,ik}),...,c({ix}{i 1,...,ik-1})]a(x)=min[c({1}-{i2....,ik}},... c{{ik){i1,...,ik-1})], where c denotes the confidence of a rule. Is the measure a a monotone, anti- monotone or non-monotone? Explain why. Hint: Use the definition of confidence and simplify the expression for aa. 1 (c) Similarly as in (b), but now we replace the minimum by the maximum. Let B(X)B(X) be the maximum confidence of all these rules: B(X)=max(c({i} {i2....,ik})....,c({ix) - {11...,ik-1))B(X)=max(c({11}-{i2....,ik})... ..c[{ik}-{i1....,ik-1}}} Is the measure BB monotone, anti-monotone or non-monotone? Explain why