SET COVERING: given a natural $k$ and a collection of finite sets
$S_1,\ldots,S_n$, is there a cover for $S_1\cup\ldots\cup S_n$ of size at most
$k$? In other words, is there a selection of at most $k$ of such sets $S_i$
such that their union equals the union of all the sets $S_1,\ldots,S_n$?
More formally, this problem can be defined as the following set:
$\{ \langle k,\langle S_1,\ldots,S_n\rangle\rangle \mid S_1,\ldots,S_n\text{ finite sets}\;\wedge\;\exists \{i_1,\ldots,i_m\}\subseteq\{1,\ldots,n\}: (m\leq k\;\wedge\;(S_1\cup\ldots\cup S_n)=(S_{i_1}\cup\ldots\cup S_{i_m})) \}$