Computational Intelligence - Problems for Chapter 4 -- Solution to part (a)

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Solution to part (a)

Yes, this is arc consistent. The relation, (X+Y) mod 2 = 1 is true of X=1, Y=4 and X=2, Y=3. For each X-value there is a Y-value and for each Y-value there is an X-value. The relation X+2 \=Z is true of X=1,Z=4 and X=2,Z=3. For each X-value there is a Z-value and for each Z-value there is an X-value. The relation Y \=Z is true of Y=3, Z=4 and Y=4,Z=3. For each Y-value there is a Z-value and for each Z-value there is an Y-value. Thus it is arc consistent, but there are no solutions!