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One of the more desirable normal forms that we can obtain is Boyce Codd normal form (BCNF) A relation schema R is in BCNF with respect to a set F of functional dependencies if, for all functional dependencies in F + of the form , where R and R, at least one of the following holds: is a trivial functional dependency (that is, ) is a superkey for schema R A database design is in BCNF if each member of the set of relation schemas that constitutes the design is in BCNF As an illustration, consider the following relation schemas and their respective functional dependencies: Customer-schema = (customer-name, customer-street, customer-city) customer-name customer-street customer-city Branch-schema = (branch-name, assets, branch-city) branch-name assets branch-city Loan-info-schema = (branch-name, customer-name, loan-number, amount) loan-number amount branch-name We claim that Customer-schema is in BCNF We note that a candidate key for the schema is customer-name The only nontrivial functional dependencies that hold on Customer-schema have customer-name on the left side of the arrow Since customer-name is a candidate key, functional dependencies with customer-name on the left side do not violate the de nition of BCNF Similarly, it can be shown easily that the relation schema Branch-schema is in BCNF The schema Loan-info-schema, however, is not in BCNF First, note that loan-number is not a superkey for Loan-info-schema, since we could have a pair of tuples representing a single loan made to two people for example, (Downtown, John Bell, L-44, 1000) (Downtown, Jane Bell, L-44, 1000)

14:01:22" "11/20/1999 14:00:04" "11/20/1999 14:00:32"

The McGraw Hill Companies, 2001

e x t e n d e d cross product an operator that builds a table consisting of all combinations of rows from each of the two input tables

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Services" "Telnet" "Oracle" "IP" "IP"

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The extended cross product operator can combine any two tables Other table combining operators have conditions about the tables to combine Because of its unrestricted nature, the extended cross product operator can produce tables with excessive data The extended cross product operator is important because it is a building block for the join operator When you initially learn the join operator, knowledge of the extended cross product opera tor can be useful After you gain experience with the join operator, you will not need to rely on the extended cross product operator The extended cross product (product for short) operator shows everything possible from two tables The product of two tables is a new table consisting of all possible combinations of rows from the two input tables Figure 34 depicts a product of two single column tables Each result row consists of the columns of the Faculty table (only FacSSN) and the columns of the Student table (only StdSSN) The name of the operator (product) derives from the

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