n-ary Relations & Their Applications

2 n-ary Relations Let A 1, A 2, …, A n be sets. An n-ary relation on these sets is a subset of A 1 x A 2 x … x A n. The A i are called the relation’s domains.

3 Example: Teaching Assignments ProfessorDepartmentCourse Number CruzZoology335 CruzZoology412 FarberPsychology501 FarberPsychology617 GrammarPhysics544 GrammarPhysics551 RosenComputer Science 518 RosenMathematics575

4 Relational Databases A relational database models a database as a relation. The relation’s domains are called its attributes. The relation’s primary key is an attribute whose value uniquely determines an element in the relation. –It is the domain of a function whose co-domain is the Cartesian product of the other domains. –In general, a primary key may consist of > 1 attribute. –What single attribute could serve as the primary key in the Teaching Assignment table?

5 Operations on n-ary Relations A selection operator defines a subset of R whose elements satisfy some the truth set of a predicate function Let the universe be the set of rows in the Teaching Assignment table (relation). Let –P( x ) mean “the professor = x” –D( x ) mean “the department = x” The Select statement below returns a set of rows or tuples { rows | P( Rosen)  D( Zoology ) }: Select Professor = “Rosen” or Department = “Zoology” selects 4 elements from Teaching Assignments.

6 To be continued