Suppose that you have a CSP containing the variables $\{$A$,$ B$,$ C$,$ D$\},$ with the domains

DA $=\{1,2,3\},$ DB $=\{1,2,3,4\},$ DC $=\{1,2\}$ and DD $=\{2,3,4,5\},$ such that the

following constraints hold:

A $<$ B$,$ A $=$ D$,$ A $=$ D $+1,$ B $>$ C$,$ B $=$ C$,$ C $+1<=$ D$.$

$($a$)$ Draw the constraint graph for this problem, and state the degree of each node.

$($b$)$ Using appropriate heuristics $($MRV$,$ degree, and LCV$)$ and stating how they are used,

show how a backtracking search $($without pruning$)$ operates to solve this problem.