(i) Frequent Itemsets via Apriori — MONKEY Dataset

Same dataset as before, min_sup = 60% (count ≥ 3), min_conf = 80%.

TID	Items
T100	M, O, N, K, E, Y
T200	D, O, N, K, E, Y
T300	M, A, K, E
T400	M, U, C, K, Y
T500	C, O, K, I, E

L1 (count ≥3)

{M}:3, {O}:3, {K}:5, {E}:4, {Y}:3

L2 (count ≥3, from valid C2 candidates)

{K,M}:3, {K,O}:3, {O,E}:3, {K,E}:4, {K,Y}:3

L3

Only candidate surviving the apriori-prune test: {K,O,E} — check: {K,O}✅ {K,E}✅ {O,E}✅ all in L2 → count in DB (T100, T200, T500) = 3 → frequent.

All frequent itemsets:

{M} {O} {K} {E} {Y}
{K,M} {K,O} {O,E} {K,E} {K,Y}
{K,O,E}

(11 itemsets total — see full step-by-step derivation in Q65's solution for the same dataset.)

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(ii) Strong Rules Matching the Metarule

Metarule: $\forall x, \text{buys}(X,\text{item}_1) \wedge \text{buys}(X,\text{item}_2) \Rightarrow \text{buys}(X,\text{item}_3)\ [s,c]$

This asks specifically for rules with exactly 2 items in the antecedent and 1 item in the consequent. The only frequent itemset large enough to produce such a rule is the 3-itemset {K, O, E} (support count = 3, support = 3/5 = 60%).

We test all three possible 2→1 splits of {K, O, E}:

Rule	Confidence = support({K,O,E}) / support(antecedent)	Strong? (≥80%)
{K,O} ⇒ E	3/3 = 100%	✅
{K,E} ⇒ O	3/4 = 75%	❌
{O,E} ⇒ K	3/3 = 100%	✅

Strong Association Rules (matching the metarule)

$$\text{buys}(X, K) \wedge \text{buys}(X, O) \Rightarrow \text{buys}(X, E) \quad [s = 60\%,\ c = 100\%]$$

$$\text{buys}(X, O) \wedge \text{buys}(X, E) \Rightarrow \text{buys}(X, K) \quad [s = 60\%,\ c = 100\%]$$

The rule {K,E} ⇒ O fails the min_conf = 80% threshold (only 75%), so it is not a strong rule and is excluded — even though {K,O,E} itself is a frequent (frequent) itemset, not every rule derived from it clears the confidence bar.