Consider the relation R, which has attributes that hold schedules of courses and sections at a university; R = {Course_no, Sec_no, Offering_dept, Credit_hours, Course_level, Instructor_ssn, Semester, Year, Days_hours, Room_no, No_of_students}. Suppose that the following functional dependencies hold on R: {Course_no} {Offering_dept, Credit_hours, Course_level} {Course_no, Sec_no, Semester, Year} {Days_hours, Room_no, No_of_students, Instructor_ssn} {Room_no, Days_hours, Semester, Year} {Instructor_ssn, Course_no, Sec_no} Try to determine which sets of attributes form keys of R. How would you normalize this relation?

Consider the following relations for an order-processing application database at ABC, Inc. ORDER (O#, Odate, Cust#, Total_amount) ORDER_ITEM(O#, I#, Qty_ordered, Total_price, Discount%) Assume that each item has a different discount. The Total_price refers to one item, Odate is the date on which the order was placed, and the Total_amount is the amount of the order. If we apply a natural join on the relations ORDER_ITEM and ORDER in this database, what does the resulting relation schema RES look like? What will be its key? Show the FDs in this resulting relation. Is RES in 2NF? Is it in 3NF? Why or why not? (State assumptions, if you make any.)

Consider the following relation: CAR_SALE(Car#, Date_sold, Salesperson#, Commission%, Discount_amt) Assume that a car may be sold by multiple salespeople, and hence {Car#, Salesperson#} is the primary key. Additional dependencies are Date_sold Discount_amt and Salesperson# Commission% Based on the given primary key, is this relation in 1NF, 2NF, or 3NF? Why or why not? How would you successively normalize it completely?