Consider a search problem with unit edge costs $($i$.$e$.,$ the cost of each edge is $1)$ and two consistent heuristic functions

h$1$ and h$2.$ Recall that a heuristic function h is consistent if it satisfies the triangle inequality:

h$($n$)<=$ c$($n$,$ n$0$

$)+$ h$($n

$0$

$)$

where c$($n$,$ n$0$

$)$ is the optimal cost between nodes n and n

$0$

$,$ and also satisfies h$($goal$)=0.$ Let h$3($n$)=$ max$($h$1($n$),$ h$2($n$))$

denote a new heuristic function.

$($d$)[3$ pts$]$ Is the heuristic function h$3$ admissible? If it is$,$ prove it$.$ If it is not, give a counter$-$example.