Fine Points

• Can't have a set cover of size smaller than n because of the ``variable'' clauses.
• Further, a size n cover will not include a positive and negative literal for the same variable. Therefore, it corresponds to an assignment.
• A size n cover will have a true variable in every clause, therefore it will correspond to a satisfying assignment.

Amazing how SAT can hide itself in other problems: set covering is just SAT in disguise!