IrMO 2015 Problem 7

Let $n > 1$ be an integer and $\Omega=\{1,2,...,2n-1,2n\}$ the set of all positive integers that are not larger than $2n$ . A nonempty subset $S$ of $\Omega$ is called sum-free if, for all elements $x, y$ belonging to $S, x + y$ does not belong to $S$ . We allow $x = y$ in this condition. Prove that $\Omega$ has more than $2^n$ distinct sum-free subsets.