We will continue to sort our fringe list as in Q$1,$ but now let f$($n$)=$ g$($n$)+$ h$($n$)$ where g$($n$)$ is the distance covered from the start state to the node n and h$($n$)$ be an admissible heuristic for node n$.$ Let C$*$ be the optimal path cost. Which of the following is correct for all nodes expanded by tree search.

Note that multiple answers may be correct. Check all correct answers.

Group of answer choices

f$($n$)<=$ C$*$

h$($n$)<=$ C$*$

g$($n$)<=$ C$*$