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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!
material, ©David Poole, Alan Mackworth and Randy Goebel, 1999