Database System Concepts
Database System Concepts
7th Edition
ISBN: 9781260084504
Author: Abraham Silberschatz, S. Sudarshan, Abraham, Henry Korth, Silberschatz Abraham, Silberschatz Professor
Publisher: McGraw-Hill Education
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Chapter 7, Problem 18PE

Explanation of Solution

To prove:

The new and original definitions of 3NF are equal.

Proof:

  • Consider the new definition of a schema given in the question in third Normal Form (3NF) along with the original one given in Section 7 3 2 of the textbook.
  • As per the definition given in Section 7 3 2 of the textbook, consider a schema R which is in 3NF.
  • By contradiction, this schema can be proved that this is in 3NF as per the new definition.
  • Let “A” be the non-primitive attribute in schema and it is transitively dependent on a key α for the schema.
  • The above statement represents β is a subset of R such that βA αβ when     Aα, Aβ and βA is not true.
  • If this is the situation, the original definition of 3NF is violated the functional dependency as,
    • Aβ represents that βA is a non-trivial functional dependency.
    • B is not a super key as βα is not true.
    • As an attribute “A” is non-prime, it is not a candidate key.
  • As per the original definition given in Section 7 3 2, the schema R can be proved that this is in 3NF

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