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Question 1. (30 pts) Suppose you would like to design a pseudocode for teaching how to play X. What would be the primitives that you would need to describe a[n)X garne? In particular, describe the syntax and semantics of primitives that you would use for playing X X Football, if your student ID is even X Basketball, if your student ID is odd Question 2. (30 pts) For the following list of values: [O] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] 5 7+c5 21 30+c3 40 46 51 60+04 101 104 108 3. How many comparisons does it take using binary search to find the following values or determine that the item is not in the list? (6, 31, 55, 108) b. What is the average. best-case and worst-case complexities of binary search algoritm in big theta notation? Give numerical examples for each case. Question 3. (40 pts) Expert Systems Construct a rule-based expert system for students, who are deciding whether to register for a coursc or not. The decision will be based on the following factors: . . whether the course is mandatory or elective, whether the student has failed the course before or not. how difficult the course is, umber of homework assignments in the course number of students who failed the course the year before. The system produces one of the following decisions: (register for the course, do not register, audit the course, take the course as pass/fail) Express the system as a decision tree with a minimum depth of 3. Show the decision path of your tree, when; 1. the course is mandatory, 2. the student has not failed the course before, 3. there are c1 HW assignments in the course, 4. and of students failed the course the year before