n -ary relations & their applications
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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
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