Suppose you have four variables A$,$ B$,$ C$,$ and D$.$ Now B$,$C$,$ and D take in values ranging from $1$ to $5.$ but A can only be assigned a value from $1$ to $4.$ In addition, whatever values they are assigned, A # B$,$ A $$C$,$B $+$C$/2,$ B $1,$ D cannot be a multiple of B$.$ Now you have to treat this problem as a constraint satisfaction problem and finalize a solution that satisfies the above$-$given scenario.

i$.$ Generate the constraint graph for this CSP

ii$.$ Formulate all the unary and binary constraints.

iii$)$ Solve the problem by employing backtracking along with forward checking. In addition, you have to use heuristics $($Variable and value ordering$)$ wherever required to select which variable to work with, and what value to assign it$.$

a$.$

Assume two variables X and Y$.$ They can be assigned any value from $0$ to $9.$ But, X has to be greater than Y$.$ What would it mean for X to be arc$-$consistent with Y$?$ And propose a solution such that X becomes arc$-$consistent with respect to Y$.$