In the water-jug puzzle we are given a 3 liter jug, named Three, and a 4 liter jug, named Four. Initially, Three and Four are empty. A jug can be filled from a tap T, and, we can discard the water from either jug into a drain, D. Water in one jug may also be poured into the other jug; however, this operation is only allowed if the receiver jug has sufficient capacity to receive the water. There are no other measuring devices. We want to find a set of operations that will leave precisely two liters of water in Four.

(a) Formulate this problem as a state-space search problem. Give a precise definition of a state, the start state, the goal state or goal condition, and the operators. Operators should be specified as "schemas" that indicate for a given state, when the operator is legal (i.e., a set of constraints on when the operator can be applied to an arbitrary state) and the description of the successor state after the operator is applied. In other words, each operator should be specified in a way that it would easily implemented in a program to solve this problem.