Write the answers on separate sheets, scan all the papers, make them as one pdf file, and upload the pdf file on the blackboard. Also upload the first page filled by you. Question 1: For the following tree, apply alpha beta pruning to find the answer at the top node. How much is the advantage if we use alpha beta pruning instead of minimax algorithm? (10 Marks) Question 2: For the following tree, (10 Marks) a) Apply stochastic minimax algorithm to the following tree to find the optimal gain by the max player at node A and what direction? b) If we multiply a constant value of 3 to all the nodes at MIN player level, will the decision of Max player change and what may be the optimal gain by the max player. Question 3: Prove that two expressions are logically equivalent. (10 Marks) i) (PQ)R ii) (RP)(RQ) Question 4: Describe all the steps of the backtracking algorithm to solve constrained satisfaction problems. How can the efficiency of the backtracking algorithm be improved? (10 Marks) Q1 Answer the following briefly (Only three to four lines are enough) a) What is the difference between the Alpha-beta pruning method and the Minimax method? b) What is the advantage of First-order logic on Propositional logic? c) Why the Minimax Algorithm can not be used for stochastic games? d) In constraint satisfaction problems, describe one method to obtain the solution? e) What are the advantages of Fuzzy logic? Q 2 (10) a) Given the following search tree, apply the alpha-beta pruning algorithm to it and show the search tree that would be built by this algorithm. Make sure that you show where the alpha and beta cuts are applied and which parts of the search tree are pruned as a result. a) Convert the following propositional logic sentence into Conjunctive Normal Form (CNF) Q3 (QP)Q b) Based on the following facts 1) Ali is the son of Amir. 2) Amir and Abdullah are brothers. 3) Nephew is the son of one's brother. Prove that Ali is the nephew of Abdullah (Use Resolution by Contradiction.)