**Go up to** 5 Arc Consistency

**Go forward to** Solution to part (b)

## 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!

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