In the set $A$ with $n$ elements, $[\sqrt{2n}]+2$ subsets are chosen such that the union of any three of them is equal to $A$. Prove that the union of any two of them is equal to $A$ as well.
Source: 239 2013 J2
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In the set $A$ with $n$ elements, $[\sqrt{2n}]+2$ subsets are chosen such that the union of any three of them is equal to $A$. Prove that the union of any two of them is equal to $A$ as well.