  For a family $\mathcal F$, let $\mathcal D(\mathcal F)$ stand for the family
of all sets that can be expressed as $F\setminus G$, where $F,G\in \mathcal F$.
A family $\mathcal F$ is intersecting if any two sets from the family have
non-empty intersection. In this paper, we study the following question: what is
the maximum of $|\mathcal D(\mathcal F)|$ for an intersecting family of
$k$-element sets? Frankl conjectured that the maximum is attained when
$\mathcal F$ is the family of all sets containing a fixed element. We show that
this holds if $n \ge 50k\ln k$ and $k \ge 50$. At the same time, we provide a
counterexample for $n< 4k$.
