AI Question $($Computer Science$)$ Given a state space graph where $A$ is the start state and $G$ is the goal state. Each

edge has its own cost and can be traversed in both directions. Heuristics h$1$ and h$2$ are

also given where $h1$ is consistent but $h2$ is not. $[23$ Marks$]$

a$)$ For each of the following strategies, mark which, if any, of the listed paths it could

return. $($Mark all paths that could be returned under some tie breaking condition.

b$)$ Consider a new heuristic function $h3$ where all the values are fixed except $h3($B$).$

Calculate the $h3(B)$ for the following conditions where non$-$negative numbers are

$0,$ and empty set is $\frac{O}{?}.$

i$.$ What values of $h3(B)$ make $h3$ admissible?

ii$.$ What values of $h3(B)$ make $h3$ consistent?