Write all the answers correctly.

$A^{*}$ and Heuristics Consider the search state graph shown below, where $S$ is a start state and $G1$ and $G2$ are goal states

$($a$)(3$ pts$)$ Which heuristics are admissible $($or write none$)?$

$($b$)(3$ pts$)$ Which heuristics are consistent $($or write none$)?$

$($c$)(3$ pts$)$ For heuristic h$1,$ what order will nodes $($paths$)$ be added to the fringe in A$$graph search?

Present info as $(($S$),$ g $+$ h $=$ f$),(($S$-$A$-$C$),12+1=13),$ etc.

$($d$)(2$ pts$)$ For heuristic h$1,$ what order will states be added to the closed$/$explored set in A$$graph$?$

$($e$)(2$ pts$)$ For heuristic h$1,$ what path with A$$graph search return?$2$ are goal states.