Chapter 6: The Relational Algebra and Relational Calculus Pre-Publication Material: This is draft manuscript yet to be copy edited or paged. Copyright AWL2004 1 CHAPTER 6: THE RELATIONAL ALGEBRA AND RELATIONAL CALCULUS Answers to Selected Exercises 6.15 Show the result of each of the example queries in Section 6.5 if they are applied to the database of Figure 5.6. Answer: (QUERY 1) Find the name and address of all employees who work for the 'Research' department. Result: FNAME LNAME ADDRESS John Smith 731 Fondren, Houston, TX Franklin Wong 638 Voss, Houston, TX Ramesh Narayan 975 Fire Oak, Humble, TX Joyce English 5631 Rice, Houston, TX (QUERY 2) For every project located in 'Stafford', list the project number, the controlling department number, and the department manager's last name, address, and birth date. Result: PNUMBER DNUM LNAME ADDRESS BDATE 10 4 Wallace 291 Berry, Bellaire, TX 20-JUN-31 30 4 Wallace 291 Berry, Bellaire, TX 20-JUN-31 (QUERY 3) Find the names of all employees who work on all the projects controlled by department number 5. Result: (empty because no tuples satisfy the result). LNAME FNAME (QUERY 4) Make a list of project numbers for projects that involve an employee whose last name is 'Smith' as a worker or as a manager of the department that controls the project. Result: PNO 1 2 (QUERY 5) List the names of all employees with two or more dependents. Result: LNAME FNAME Smith John Wong Franklin (QUERY 6) List the names of employees who have no dependents. Result: LNAME FNAME Zelaya Alicia Narayan Ramesh English Joyce Jabbar Ahmad Borg James (QUERY 7) List the names of managers who have at least one dependent.Chapter 6: The Relational Algebra and Relational Calculus Pre-Publication Material: This is draft manuscript yet to be copy edited or paged. Copyright AWL2004 2 Result: LNAME FNAME Wallace Jennifer Wong Franklin 6.16 Specify the following queries on the database schema shown in Figure 5.5 using the relational operators discussed in this chapter. Also show the result of each query if applied to the database of Figure 5.6. (a) Retrieve the names of employees in department 5 who work more than 10 hours per week on the 'ProductX' project. (b) List the names of employees who have a dependent with the same first name as themselves. (c) Find the names of employees that are directly supervised by 'Franklin Wong'. (d) For each project, list the project name and the total hours per week (by all employees) spent on that project. (e) Retrieve the names of employees who work on every project. (f) Retrieve the names of employees who do not work on any project. (g) For each department, retrieve the department name, and the average salary of employees working in that department. (h) Retrieve the average salary of all female employees. (i) Find the names and addresses of employees who work on at least one project located in Houston but whose department has no location in Houston. (j) List the last names of department managers who have no dependents. Answers: In the relational algebra, as in other languages, it is possible to specify the same query in multiple ways. We give one possible solution for each query. We use the symbol s for SELECT, P for PROJECT, J for EQUIJOIN, * for NATURAL JOIN, and f for FUNCTION. (a) EMP_W_X <-- ( s PNAME='ProductX' (PROJECT)) J (PNUMBER),(PNO) (WORKS_ON) EMP_WORK_10 <-- (EMPLOYEE) J (SSN),(ESSN) ( s HOURS>10 (EMP_W_X)) RESULT <-- P LNAME,FNAME ( s DNO=5 (EMP_WORK_10)) Result: LNAME FNAME Smith John English JoyceChapter 6: The Relational Algebra and Relational Calculus Pre-Publication Material: This is draft manuscript yet to be copy edited or paged. Copyright AWL2004 3 (b) E <-- (EMPLOYEE) J (SSN,FNAME),(ESSN,DEPENDENT_NAME) (DEPENDENT) R <-- P LNAME,FNAME (E) Result (empty): LNAME FNAME (c) WONG_SSN <-- P SSN ( s FNAME='Franklin' AND LNAME='Wong' (EMPLOYEE)) WONG_EMPS <-- (EMPLOYEE) J (SUPERSSN),(SSN) (WONG_SSN) RESULT <-- P LNAME,FNAME (WONG_EMPS) Result: LNAME FNAME Smith John Narayan Ramesh English Joyce (d) PROJ_HOURS(PNO,TOT_HRS) <-- PNO f SUM HOURS (WORKS_ON) RESULT <-- P PNAME,TOT_HRS ( (PROJ_HOURS) J (PNO),(PNUMBER) (PROJECT) ) Result: PNAME TOT_HRS ProductX 52.5 ProductY 37.5 ProductZ 50.0 Computerization 55.0 Reorganization 25.0 Newbenefits 55.0 (e) PROJ_EMPS(PNO,SSN) <-- P PNO,ESSN (WORKS_ON) ALL_PROJS(PNO) <-- P PNUMBER (PROJECT) EMPS_ALL_PROJS <-- PROJ_EMPS -:- ALLPROJS (* DIVISION operation *) RESULT <-- P LNAME,FNAME (EMPLOYEE * EMP_ALL_PROJS) Result (empty): LNAME FNAME (f) ALL_EMPS <-- P SSN (EMPLOYEE) WORKING_EMPS(SSN) <-- P ESSN (WORKS_ON) NON_WORKING_EMPS <-- ALL_EMPS - WORKING_EMPS (* DIFFERENCE *) RESULT <-- P LNAME,FNAME (EMPLOYEE * NON_WORKING_EMPS) Result (empty): LNAME FNAME (g) DEPT_AVG_SALS(DNUMBER,AVG_SAL) <-- DNO f AVG SALARYChapter 6: The Relational Algebra and Relational Calculus Pre-Publication Material: This is draft manuscript yet to be copy edited or paged. Copyright AWL2004 4 (EMPLOYEE) RESULT <-- P DNUMBER,AVG_SAL ( DEPT_AVG_SALS * DEPARTMENT ) Result: DNUMBER AVG_SAL Research 33250 Administration 31000 Headquarters 55000 (h) RESULT(AVG_F_SAL) <-- f AVG SALARY ( s SEX='F' (EMPLOYEE) ) Result: AVG_F_SAL 31000 (i) E_P_HOU(SSN) <-- P ESSN (WORKS_ON J(PNO),(PNUMBER) ( s PLOCATION='Houston' (PROJECT))) D_NO_HOU <-- P DNUMBER (DEPARTMENT) - P DNUMBER ( s DLOCATION='Houston' (DEPARTMENT)) E_D_NO_HOU <-- P SSN (EMPLOYEE J(PNO),(DNUMBER) (D_NO_HOU)) RESULT_EMPS <-- E_P_HOU - E_D_NO_HOU (* this is set DIFFERENCE *) RESULT <-- P LNAME,FNAME,ADDRESS (EMPLOYEE * RESULT_EMPS) Result: LNAME FNAME ADDRESS Wallace Jennifer 291 Berry, Bellaire, TX (j) DEPT_MANAGERS(SSN)<-- P MGRSSN (DEPARTMENT) EMPS_WITH_DEPENDENTS(SSN) <-- P ESSN (DEPENDENT) RESULT_EMPS <-- DEPT_MANAGERS - EMPS_WITH_DEPENDENTS RESULT <-- P LNAME,FNAME (EMPLOYEE * RESULT_EMPS) Result: LNAME FNAME Borg James 6.18 Consider the LIBRARY relational schema shown in Figure 7.20, which is used to keep track of books, borrowers, and book loans. Referential integrity constraints are shown as directed arcs in Figure 7.20, as in the notation of Figure 7.7. Write down relational expressions for the following queries on the LIBRARY database: (a) How many copies of the book titled The Lost Tribe are owned by the library branch whose name is "Sharpstown"? (b) How many copies of the book titled The Lost Tribe are owned by each library branch? (c) Retrieve the names of all borrowers who do not have any books checked
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