n-ary Relations & Their Applications

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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.

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Example: Teaching Assignments

Professor Department Course Number

Cruz Zoology 335

Cruz Zoology 412

Farber Psychology 501

Farber Psychology 617

Grammar Physics 544

Grammar Physics 551

Rosen Computer Science

518

Rosen Mathematics 575

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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?

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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.

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To be continued