Minimum number of sets – mathoverflow.net

Let $\mathcal{F}$ be a union-closed family with universe (the union of all sets in $\mathcal{F}$) $U(\mathcal{F}) = [m] = \{1, \ldots, m\}$, and $7 \le m \le |\mathcal{F}|/2$. Let $\mathcal{F}_X = {A ...