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n -ary Relations & Their Applications. 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. Example: Teaching Assignments. Relational Databases.
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n-ary Relations • Let A1, A2, …, An be sets. • An n-ary relation on these sets is a subset of A1 x A2 x … x An. • The Ai are called the relation’s domains.
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?
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”orDepartment = “Zoology” selects 4 elements from Teaching Assignments.
