1. In the graph below are the arcs {x,y) and (y,x} are consistent? Explain why they are consistent or inconsistent. Adjust the graph to be arc consistent and draw the updated graph. X>y x = {1, ..., 5} y = {2, ..., 6} 2. Consider the below constraint network, formulate the constraint satisfaction problem. What can be the possible reduced domain values for each variable in the network? {1,2}A B {2,3} {1,2,3} ){1,2,3} E {1,2} 3. Assume that you are in the third year of your undergraduate program. You are having Artificial Intelligence class weekly three days (Monday's, Wednesday's and Friday's) In total there are five bathes in a week and 3 teachers will be handling the classes. There is a constraint that each teacher can handle only one batch at a time. The batch timings are Batch 1: from 8:00-9:00am Batch 2: from 8:30-9:30am Batch 3: 9:00-10:00am Batch 4: 9:30-10:30am Batch 5: from 9:30-10:30am The teachers can handle batches as follows Teacher A: available to teach for batches 3 and 4. Teacher B: Available to teach for batches 2, 3, 4, and 5. Teacher C: Available to teach for batches 1, 2, 3, 4, 5. i) ii) iii) Articulate the above problem as a Constraint Satisfaction Problem. Draw a CSP graph Check whether the network is arc consistent. If not, run the arc consistency and show the reduced graph. Give possible solutions to the CSP problem. iv)