nary Relations Their Applications nary Relations Let A

n-ary Relations & Their Applications

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

Example: Teaching Assignments Professor Cruz Farber Grammar Rosen Department Zoology Psychology Physics Computer Science Mathematics Course Number 335 412 501 617 544 551 518 575 3

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? 4

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. 5

To be continued 6