Mathematics Question from JEE Main 2025 · 7 April, Shift 1

For $n \geq 2$, let $S_n$ denote the set of all subsets of $\{1, 2, 3, \ldots, n\}$ with no two consecutive numbers. For example, $\{1, 3, 5\} \in S_6$, but $\{1, 2, 4\} \notin S_6$. Then, find $n(S_5)$.