Harsha Data mining dis – i need a discussion on the below topic

I need help with a Writing question. All explanations and answers will be used to help me learn.

The following questions examine how the support and confidence of an association rule may vary in the presence of a concept hierarchy.

(a) Consider an item x in a given concept hierarchy. Let x1, x2, …, xk denote the k children of x in the concept hierarchy. Show that s(x) ≤ k i=1 s(xi), where s(·) is the support of an item. Under what conditions will the inequality become an equality?

(b) Let p and q denote a pair of items, while ˆp and ˆq are their corresponding parents in the concept hierarchy. If s({p, q}) > minsup, which of the following itemsets are guaranteed to be frequent? (i) s({p, q ˆ }), (ii) s({p, qˆ}), and (iii) s({p, ˆ qˆ}).

(c) Consider the association rule {p} −→ {q}. Suppose the confidence of the rule exceeds minconf. Which of the following rules are guaranteed to have confidence higher than minconf? (i) {p} −→ {qˆ}, (ii) {pˆ} −→ {q}, and (iii) {pˆ} −→ {qˆ}.

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