The following constraint graph represents the three constraints $($i$)A,B$ and $D$ are not greater than $C,$

$($ii$)B$ is $A+2$ and $($ii$)B$ is less that $D.$ The domain of $A,B,C$ and $D$ is $\{4,5,6,7\}.$

a$.[5$ pts$]$ Run arc consistency on the arc from A to B$.$ What values on A remain viable after this

operation?

b$.[5$ pts$]$ Assuming there were no arcs left in the list of arcs to be processed, which arc$($s$)$ would be

added to the queue for processing after this operation?

c$.[10$ pts$]$ Using arc consistency method on all arc, find the feasible values for A$,$ B$,$ C and D$.$ Show

all your work.