onstraint propagation $(6$ points$)$

Consider the CSPs represented by the constraint networks below:

x y

$($x$+$y$)$ is odd

$\{1,2\}$

$\{3,4\}$

x y

$($x$+$y$)$ is odd

$\{1,2\}$

$\{2,4\}$

z

x$+2$ z y z

$\{3,4\}$

z

x$+2$ z y z

$\{3,4\}$

CSP I CSP II

For each CSP$,$

$1.$ State whether or not the CSP is arc$-$consistent.

$2.$ If it is$,$ explain why.

$3.$ If it is not, explain which domain must be reduced to make the CSP arc$-$consistent, and specify the

constraint that can be used to reduce the domain.