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Understanding Relational Algebra and Calculus Operations in Database Management

This chapter explores critical operations in relational algebra and relational calculus, focusing on SELECT, PROJECT, UNION, INTERSECTION, and JOIN operations. It presents various figures illustrating the results of these operations, including examples of queries such as extracting specific attributes and applying filters. Additionally, the chapter covers Cartesian products, natural joins, and the division operation in detail. These foundational concepts are essential for effectively managing and querying relational databases, providing a comprehensive understanding of their functionality.

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Understanding Relational Algebra and Calculus Operations in Database Management

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  1. Chapter 6 The Relational Algebra and Relational Calculus

  2. FIGURE 6.1Results of SELECT and PROJECT operations. (a) s(DNO=4 AND SALARY>25000) OR (DNO=5 AND SLARY>30000)(EMPLOYEE). (b) pSEX, SALARY(EMPLOYEE).

  3. FIGURE 6.2Results of a sequence of operations. (a) pFNAME, LNAME, SALARY(sDNO=5(EMPLOYEE)). (b) Using intermediate relations and renaming of attributes.

  4. FIGURE≈6.3Results of the UNION operation RESULT € RESULT1  RESULT2.

  5. FIGURE≈6.4The set operations UNION, INTERSECTION, and MINUS. (a) Two union-compatible relations. (b) STUDENT  INSTRUCTOR. (c) STUDENT  INSTRUCTOR. (d) STUDENT – INSTRUCTOR. (e) INSTRUCTOR – STUDENT

  6. FIGURE≈6.5aThe CARTESIAN PRODUCT (CROSS PRODUCT) operation.

  7. FIGURE≈6.5bThe CARTESIAN PRODUCT (CROSS PRODUCT) operation.

  8. FIGURE≈6.5cThe CARTESIAN PRODUCT (CROSS PRODUCT) operation.

  9. FIGURE≈6.6Result of the JOIN operation DEPT_MGR  DEPARTMENT JOIN MGRSSN=SSN EMPLOYEE .

  10. FIGURE≈6.7Results of two NATURAL JOIN operations. (a) PROJ_DEPT  PROJECT * DEPT. (b) DEPT_LOCS  DEPARTMENT * DEPT_LOCATIONS.

  11. FIGURE≈6.8The DIVISION operation. (a) Dividing SSN_PNOS by SMITH_PNOS. (b) T R ÷ S.

  12. FIGURE≈6.9The AGGREGATE FUNCTION operation.

  13. FIGURE≈6.10A two-level recursive query.

  14. FIGURE≈6.11The result of a LEFT OUTER JOIN operation.

  15. FIGURE≈6.12A relational database schema for a LIBRARY database.

  16. FIGURE≈6.13A database state for the relations T1 and T2.

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