Question 1: a) For cach of the following tasks, Choose a formulation that is precise enough to be implemented and mention the initial state goal test, successor function, and cost function: 1 - Coloring a planar map using four colors in such a way that no two adjacent regions have the same color 2- A 3-foot tall monkey is in a room where bananas are suspended from the 8-foot ceiling. The monkey wants to get the bananas and the room contains two stackable, movable, climbable 3-foot high crates 3- A program outputs the message illegal input record" when fed a certain file of input records. You know that processing of cach record is independent of the other records. You want to discover what record is illegal. 4- You have 3 jugs, measuring 12 gallons, 8 gallons, and 3 gallons, and a water faucet. You can fill the jugs up or empty them out from one to another or onto the ground. You need to measure out exactly one gallon