Relational Algebra

Set operations: Union, intersection, difference, Cartesian product Relational operations: Selection, projection, join, division

Union Set1={A, B, C} Set2={C, D, E} Union: Members in Set 1 or in Set 2 –Set1 U Set 2 = {A, B, C, D, E} Or

Intersect Members in Set 1 and in Set 2 –Set1 ∩ Set2={C} And

Difference Set1 – Set2: Members in Set1 but not in set2 = {A,B} Set2 – Set1:Members in Set2 but not in set1 = {D, E} Set1-Set2 ≠ Set2 – Set1

Union Compatibility Two relations that have the same number of attributes and same type of attributes. Union, Intersect and difference operators require the two relations to be union compatible.

File 1: –SID – 9 characters –Sname – 25 characters File 2: –SSN – 9 characters –Ename – 25 characters File 3: –Ename – 25 characters –EID – 9 characters

Use Union and Difference to Simulate Intersect Set1 ∩ Set2 = Set1 – (Set1 – Set2)

Venn Diagram Set 1: Major = ‘Business’ Set 2: Sex = ‘F’ Set 3: GPA > 3.0

Files as Sets Business students’ file: BusSt Science student’s file: SciSt –BusSt U SciSt: –BusSt ∩ SciSt –BusSt – SciSt Spring 04 Student file: S04St Fall 04 Student file: F04St –S04St – F04St –F04St – S04St

Product Set1 = {a, b, c} Set2 = {X, Y, Z} Set1 X Set2 = {aX, aY aZ, bX, bY, bZ, cX, cY, cZ}

Faculty File: FIDFname F1Chao F2Smith Student File: SIDSname FID S1PeterF1 S2PaulF2 S3SmithF1 Faculty X Student:

Selection Selection operation works on a single relation and defines a relation that contains records that satisfy the criteria. – σ criteria ( Relation) – σ Major = ‘Bus’ AND GPA > 3.0 (Student)

Projection Projection operation works on a single relation and defines a vertical subset of the relation, extracting the values of specified attributes and eliminating duplicates. π a1, a2, … (Relation) π sid, sname (Student)

Student file: SID, SnameSexMajor S1PeterMBus S2PaulMArt S3MaryFBus S4NancyFSci S5PeterMArt π sid, sname (Student) π sname, sex (Student) π sname, sex ( σ Major = ‘Bus’ (Student)) σ Major = ‘Bus’ ( π sname, sex (Student))

Duplications due to Projection WorkLog file: EIDPjIDHours E1P25 E1P14 E2P26 E2P18 E3P14 π eid (WorkLog) Relation contrains: no duplication Eliminating duplicates may cause problems: –π Hours ( σ PjID = ‘P1 (WorkLog)) In practice, users determine whether to eliminate duplicates: –SELECT DISTINCT EID FROM WorkLog; –SELECT HOURS FROM WorkLog WHERE PjID = ‘P1’;

Natural Join The two relations must have common attributes. Combines two relations to form a new relation where records of the two relations are combined if the common attributes have the same value. One occurrence of each common attribute is eliminated.

Faculty File: FIDFname F1Chao F2Smith Student File: SIDSname FID S1PeterF1 S2PaulF2 S3SmithF1 Faculty Join Student = π All except the duplicated attributes (σ Faculty.FID = Student.FID ( Faculty X Student )) Note: Use RelationName.FieldName to make a field name unique.

Examples University database: –Student: SID, Sname, Sex, Major, GPA, FID –Account: SID, Balance –Faculty: FID, Fname –Course: CID, Cname, Credits –StudentCourse: SID, CID