The number of triples of sets (A,B,C) with\(A, B, C \subseteq \{1, 2, \dots, n\}\) Such that \((A \cap B) \subseteq C \subseteq (A \cup B)\)
Decide independently for each element x of {1, …, n}, based on where it sits relative to A and B:
Total per element = 1 + 1 + 2 + 2 = 6, so the number of triples is \(6^n\).
Answer: (B) \(6^n\)
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