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Erdős problem 447

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How large can a union-free collection F\mathcal{F} of subsets of [n][n] be? By union-free we mean there are no solutions to A∪B=CA\cup B=C with distinct A,B,C∈FA,B,C\in \mathcal{F}. Perhaps even ∣F∣<(1+o(1))(n⌊n/2⌋)?\lvert \mathcal{F}\rvert <(1+o(1))\binom{n}{\lfloor n/2\rfloor}?

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