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Question 1 (Relational Algebra) [25 points] Consider the following relations. The primary keys are underlined. All attributes are of type string if not indicated otherwise. [Hint: Use multi-step and multi-line queries to ease the formulation of queries. Use the rename operator ρ to give intermediate query results a name (some textbooks use the equivalent ‘←’ notation). Aggregate functions as you can find them defined in some textbooks are not allowed. • Student(sID, name, degree: integer, dID) • Department(dID, name, address) • Lecture(lID, name, degree: integer, pID, dID) • Professor(pID, name, dID) • Register(rID, sID, lID, Semester, score: integer) (a) [5 points] Find the names of students who have registered every lecture of CISE department. (b) [5 points] Find the students who got the highest score in the lecture ‘DB’ in 2021 Fall semester. Show names and scores together. (c) [5 points] Find the names of students in CISE department who never received a score less than 80. (d) [5 points] Find the names of students who got more than 90 in the ‘DB’ lecture and less than 70 in the ‘Algorithm’ lecture. (e) [5 points] Find the names of departments whose lectures were taught by professors of other depart- ments. 2 Question 2 (Relational Algebra) [30 points] Consider the following relations. The primary keys are underlined. All attributes are of type string if not indicated otherwise. [Hint: Use multi-step and multi-line queries to ease the formulation of queries. Use the rename operator ρ to give intermediate query results a name (some textbooks use the equivalent ‘←’ notation). Aggregate functions as you can find them defined in some textbooks are not allowed. • Book(bID, title, author, publisher, year, price) • Customer(cID, name, SSN, gender, email) • CreditCard(ccID, cID, number, exprDate) • BookOrder(oID, bID, ccID, quantity: integer, date) (a) [5 points] Find the titles of books that were ordered by the customers John or Jane. Assume John and Jane are unique. (b) [5 points] Find the dates of the orders when John’s credit card was used. (c) [5 points] Find the names of publishers whose books are not sold yet. (d) [5 points] Find the information of customers(name and email) who have credit cards that have been never used. Show their never-used credit card numbers as well. Assume a customer can have multiple credit cards. The customers have ordered before(with other credit cards). (e) [5 points] Find the names of customers who have orders a ‘DB’ book more than once. (f) [5 points] Find the information of the most expensive ‘DB’ book. List the title, author, publisher, year, and price. 3 Question 3 (Relational Algebra) [20 points] Consider the following relations. The primary keys are underlined. All attributes are of type string if not indicated otherwise. [Hint: Use multi-step and multi-line queries to ease the formulation of queries. Use the rename operator ρ to give intermediate query results a name (some textbooks use the equivalent ‘←’ notation). Aggregate functions as you can find them defined in some textbooks are not allowed. • Customer(cID, name, SSN, age: integer, gender, address, email) • Gym(gID, name, location, withPool: [‘Y’ or ‘N’], price: integer, pet: [‘Y’ or ‘N’]) • Guest(gsID, name, cID, age: integer, gender, email) • Member(cID, gID) • GuestVisit(gsID, date) (a) [5 points] Find the names and ages of customers who are members of every gym in Gainesville. (b) [5 points] Find the names of gyms that satisfy the following conditions. 1. It allows a pet. 2. It costs less than $50. 3. It does not allow a guest to its members (Assumption: At least one guest’s information is stored if a gym allows guests.) (c) [5 points] Find the names of members along with gym names whose gym has a pool and costs more than $100. (d) [5 points] Find the names of customers whose guests visit gyms more than once. 4 Question 4 (Relational Algebra) [25 points] The following questions let you think deeper about the concepts of the Relational Algebra. (a) [5 points] Let R be the schema of a relation R, and let A1, . . . ,An ⊆ R. Is the Relational Algebra expression πA1(πA2(. . .(πAn(R)) . . .)) correct, in general? If yes, argue why. If not, argue why not. If your answer is no, are there any restrictions that could make the statement true? If so, what are these restrictions in mathematical notation? (b) [5 points] Let R be the schema of a relation R, and let A⊆R. What is the condition in mathematical notation such that πA(σF(R)) = σF(πA(R)) holds where F is assumed to be a correct predicate on R? (c) [15 points] Let R(A,B,C), S(B,D), and T (A,C) be relations such that R has r tuples, S has s tuples, and T has t tuples with r > 0, s > 0, and t > 0. The attributes A,B,C, and D are supposed to have the same numerical data type. Consider the given Relational Algebra expressions below and determine the minimum number and the maximum number of possible tuples of each result relation. Explain your answers. (1) [5 points] πA, C(R)∩T (2) [5 points] R 1R.B=S.B S (3) [5 points] πB(πB(R)∪ πB(S)) (For this question, also consider two other possible numbers of tuples beside the minimum and maximum number of tuples.) 5