n-ary Relations

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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 relations 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 relations domains are called its attributes.
• The relations 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 gt 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