  Let $F$ be a graph. We say that a hypergraph $H$ contains an induced Berge
$F$ if the vertices of $F$ can be embedded to $H$ (e.g., $V(F)\subseteq V(H)$)
and there exists an injective mapping $f$ from the edges of $F$ to the
hyperedges of $H$ such that $f(xy) \cap V(F) = \{x,y\}$ holds for each edge
$xy$ of $F$. In other words, $H$ contains $F$ as a trace.
  Let $ex_{r}(n,B_{ind} F)$ denote the maximum number of edges in an
$r$-uniform hypergraph with no induced Berge $F$. Let $ex(n,K_r, F)$ denote the
maximum number of $K_r$'s in an $F$-free graph on $n$ vertices. We show that
these two Tur\'an type functions are strongly related.
