Which of the following state spaces shows an ADMISSIBLE h$($s$)$ function? The state spaces all have the same arcs to the same states, with the same action costs. The only difference among them is their h$($s$)$ function values. In case the fonts do not display well, h$($G$)=0$ for all state spaces, and h$($S$)=10$ for all state spaces.

To answer this question, you need to review what is the definition of ADMISSIBILITY. An h$()$ function is admissible only if it never overestimates the cost of the cheapest path from any state to a goal state. HINT: You'll need to look at the g$()$ values as well as h$()$ values, and remember that the cost of a path is the sum of all the g$()$ values along that path.