# Solution: 2021-21 Different unions

Let $$F$$ be a family of nonempty subsets of $$[n]=\{1,\dots,n\}$$ such that no two disjoint subsets of $$F$$ have the same union. In other words, for $$F =\{ A_1,A_2,\dots, A_k\},$$ there exists no two sets $$I, J\subseteq [k]$$ with $$I\cap J =\emptyset$$ and $$\bigcup_{i\in I}A_i = \bigcup_{j\in J} A_j$$. Determine the maximum possible size of $$F$$.

For the new version of POW 2021-21, the best solution was submitted by 이재욱 (전기및전자공학부 2018학번, +4). Congratulations!

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