I was reading some bachelor thesis and it mentioned reducing the hitting set problem to the set cover problem. However I am unable to understand the last line in the referenced paragraph, I would really appreciate if someone can help clarify it. Here is the paragraph:
In order to reduce the hitting set problem to the set cover problem. Let us think of a function having an instance S for the hitting set problem which will map it to U and F as instances to the set cover problem as follows.
$$f (S) = (U, F )$$
where $U = S$,
$F = ${$A_i |i \in U_S$}
where $U_S = \cup_{B∈S}B, A_i = ${$B|B \in S \ \& \ i\in B\}$
Thanks in advance.