Question 167
Let $S$ be a set of integers. We say that $S$ is sum-free if, for all integers $x$ and $y$ belonging to $S$, the sum $x+y$ does not belong to $S$. For every integer $n \geqslant 1$, denote by $s_{n}$ the number of subsets of $\{1,2, \ldots, 2 n\}$ that are sum-free.
Prove that $s_{n} \geqslant 2^{n}$.
Prove that $s_{n} \geqslant 2^{n}$.