Parts $($c$),($d$),$ and $($e$)$ Consider a search problem where all edges have cost $1$ and the optimal solution

has cost $C.$ Let $h$ be a heuristic which is max$\{h^{**}-k,0\},$ where $h^{**}$ is the actual cost to the closest goal and $k$

is a nonnegative constant.

$($c$)(2$ pt$)$ Circle all of the following that are true $($if any$).$

$($i$)h$ is admissible.

$($ii$)h$ is consistent.

$($iii$)A^{**}$ tree search $($no closed list$)$ with $h$ will be optimal.

$($iv$)A^{**}$ graph search $($with closed list$)$ with $h$ will be optimal.