  We show that there exists an absolute constant $C>0$ such that any family
$\mathcal{F}\subset \{0,1\}^n$ of size at least $Cn^3$ has dual VC-dimension at
least 3. Equivalently, every family of size at least $Cn^3$ contains three sets
such that all eight regions of their Venn diagram are non-empty. This improves
upon the $Cn^{3.75}$ bound of Gupta, Lee and Li and is sharp up to the value of
the constant.
