= Solution
\b[Yes: $h_1(R)=|R|$ is an <admissible heuristic>.] One application of the <resolution inference rule> removes just one current negative <Boolean literal>. It may add other negative <Boolean literals>, and some of those may already occur, but it cannot remove any other current obligation. Consequently
$$
|R'|\ge |R|-1.
$$
If $\ell$ actions lead from $R$ to $\varnothing$, applying this inequality at every step gives $0\ge |R|-\ell$. Thus
$$
\boxed{h_1(R)=|R|\le\ell,\qquad h_1(R)\le h^*(R).}
$$
It is also a <consistent heuristic>, since $h_1(R)\le1+h_1(R')$ and $h_1(\varnothing)=0$. In particular, merging duplicate obligations cannot invalidate the lower bound: removing several duplicates from the representation never counts as removing several distinct members of a <set>.
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