Combinatorial problems in finding the number of subsets of $S_n$

Asked Dec 08 '18 at 15:19

Active Dec 08 '18 at 15:19

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For $A \subset \mathbb{R}$, let $A'=\{a+1|a \in A\}$. Let $S_n=\{1;2;3;...;n\}$. How many subsets $A$ of $S_n$ satisfying $A \cup A' = S_n$?

I'm trying to solve this problem by using bijection or constructing a sequence but still struggling. Please help me with this.

asked Dec 08 '18 at 15:19

Steven Tran

Have you tried making examples for small $n?$ – saulspatz Dec 08 '18 at 15:45
Hint: You can find a recurrence for your answer by conditioning on whether or not $n\in A$. – Mike Earnest Dec 08 '18 at 17:47
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See https://math.stackexchange.com/questions/261326/how-many-n-digits-binary-numbers-can-be-formed-where-0-is-not-repeated. – Anubhab Dec 08 '18 at 18:23

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