$3.$Computer Science$/$AI question. Adam, Barb, Camellia, and David are picking their entrees at a restaurant. The entrees are egg, falafel, granola, and hamburger. They have some strict dietary preferences:

$$ Camellia will not order hamburger.

$$ Adam and Barb want to steal each other$$s food, which is pointless if they both order the same dish. So$,$ Adam and Barb will order different dishes.

$$ Barb will only order egg or granola.

$$ Camellia likes to be unique in her food orders and will not order the same dish as anybody else, with one exception. Adam and Camellia are twins, and always order same dish as each other.

$$ David really dislikes falafel and will not order it$.$

i$.$ Draw the corresponding constraint graph for this CSP$.$

ii$.$ Run basic backtracking search to solve this CSP and make sure that every variable $($person$)$ is matched with their value $($dream dish$).$ Consider alphabetical order to select unassigned variables and to iterate over values. What assignment will backtracking search return?

iii. Assume that no values have been assigned to the variables and we are doing the one iteration of forward checking. Write down the value$($s$)$ that will be eliminated if we assign $$egg$$ to Adam. If no values will be eliminated, then write $$None$.$

$$ Value$($s$)$ that will be eliminated for Barb: $\_\_\_\_\_\_\_\_\_\_\_$

$$ Value$($s$)$ that will be eliminated for Camellia: $\_\_\_\_\_\_\_\_\_\_\_\_$

$$ Value$($s$)$ that will be eliminated for David: $\_\_\_\_\_\_\_\_\_\_\_\_$