Let n be an integer, n ≥ 3. A certain mathematical theorem asserts that n statements A1, A2,‖, An are equivalent.
(a) A student proves this by showing that A1 ↔ A2, A2 ↔ A3,‖, An-1 ↔ An are all true. How many implication proofs did the student write down?
(b) Another student proves the truth of A1 → A2, A2 → A3, ‖, An-1 → An, and An → A1. How many implication proofs did this student write down?
(c) A third student wishes to find a proof that is different from that in 11(b) but uses the same number of implication proofs as in 11(b). Outline a possible proof for this student.
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