2. For n E N, let Xn be the set of non-empty subsets of {1, 2, 3, . .., n} which do not contain any two consecutive integers. For example, X1 = {{1} } X2 = {{1}, {2} } X3 = {{1}, {2}, (3}, {1, 3} } X4 = {{1}, {2}, (3), {4}, {1, 3}, {1, 4}, {2, 4} }. For a finite subset A of N, let f(A) : Ia2. aEA For example, f ({1, 3, 8, 17}) = 12 . 32 . 82 . 172. Let an : I f (A ) . AEXn Question: Show that a2024 = (2025)! - 1 Hint: Use induction