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Solution to part (a)

Is the arc <X,Y> arc consistent? no. Arc <X,Y> is arc consistent means that for every X there exists a Y such that r(X,Y) is true. The following table shows for each value of X a value of Y such that R(X,Y) is true:
There is no element Y in {a,d,i,r} such that r(c,Y) is true. That is there is no word starting with ca, cd, ci, or cr in the word list. c can be removed from the domain of X to make <X,Y> arc consistent.
Computational Intelligence online material, ©David Poole, Alan Mackworth and Randy Goebel, 1999

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