Q1. Given a full 5-gallon jug and an empty 2-gallon jug, the aim is to fill the 2-gallon jug with exactly one gallon of water. You might use the given state space formulation.

State = (x, y), where x is the number of gallons of water in 5-gallon jug and y is the number of gallons in 2-gallon jug.
Initial State = (5, 0)
Goal State = (*, 1), where * means any amount
Make the search tree. Describe which search strategy is suitable for this problem.

Q2. Assume that a knowledge base KB which comprises the given propositional logic sentences:

Q ⇒ P
P ⇒ ¬Q
QvR

a) Construct a truth table which shows the truth value of each sentence in KB and point out the models in which the KB is true.

b) Does KB entail R? Utilize the definition of entailment to validate your answer.

c) Does KB entail R ⇒ P? Expand the truth table and employ the definition of entailment to validate your answer.

d) Does KB entail Q ⇒ R? Expand the truth table and employ the definition of entailment to validate your answer.