Problem $3$: AC$-3$ Algorithm $(7$ pts$.)$

Let assume we have the following constraint graph.

a$)$ Write down the binary constraints for the graph.

$AB$

b$)$ Suppose you only have three colors to color this graph: Red, Blue, and Yellow. Start with node$-$A$,$ assign the

color red; assign the color yellow for node$-$D; and for node$-$G$,$ assign the color blue. Run the AC$-3$ algorithm over

the graph. Show the state of the assignment at each step.