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6 Arc Consistency

Suppose you have a relation r(X,Y) that is true of there is a word in the word list below with first letter X and second letter Y. The word list is:

add arc bad bud

cup dip fad odd

Suppose the domain of X is {a,b,c,d} and that of Y is {a,d,i,r}.

Is the arc <X,Y> arc consistent? If so, explain why. If not, show what element(s) can be removed from a domain to make it arc consistent.
Is the arc <Y,X> arc consistent? If so, explain why. If not, show what element(s) can be removed from a domain to make it arc consistent.

Solution to part (a)

Solution to part (b)