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 36E

Explanation of Solution

BCNF (Boyce Codd Normal Form):

A relation is said to be in BCNF if it holds the following 2 conditions:

  • The relation is in Third Normal Form
  • For every dependency X→a, X is superkey.

Every binary relation which means every schema consisting of exactly 2 attributes is said to be in BCNF.

In order to prove that, consider all possible combinations of functional dependencies on a relation R with 2 attributes A1 and A2.

Case1: A1→A2

In this case, A1 is the candidate key and hence also a superkey as candidate keys is minimal superkeys.

So, the BCNF condition satisfies in this case...

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