$1.$ Preliminary Questions:

A$.$ What is the difference between uninformed and informed search?

B$.$ What is a heuristic?

C$.$ When is a heuristic admissible?

$2.$ In the following graph, a is the start node and e is the goal node. Each node n is labelled with the values for f$($n$)$ and h$($n$),$ listed as a pair $[$f$,$ h$].$ Remember that f$($n$)=$ cost$($n$)+$ h$($n$).$

Given this information, determine the cost of each arc. The cost of arc a $-$ c has already been listed for you $($it has a cost of $2).$ Label the arcs in the diagram.

$3.$ Is the heuristic h admissible in the previous graph? Why or why not?