Normalization solved exercise 4

Set of solved exercises in Normalization / Normalization Solved Examples / How to find candidate keys, and primary keys in database? / Sets of examples to find the keys of a tables / Process of Key finding in a database – Examples / Normalization to BCNF.

Question:

Consider a relation R(A, B, C) with FD's AB → C, AC → B, BC → A.

Determine all the keys of relation R. Is the relation R in BCNF?

Solution:

From AB → C, we obtain that AB is one of the keys.

From AC → B, we obtain that AC is one of the keys.

From BC → A, we obtain that BC is one of the keys.

Every single FD given above, includes all the attributes of R. Hence, all the left hand side attributes form the key. And the keys are AB, AC, and BC.

Is R in BCNF?

Requirements: R should be in 2NF, 3NF, and every determinant must be a candidate key.

From the set of functional dependencies given, we observe the following;

• No partial key dependencies. So, R is in 2NF.
• No transitive dependencies. So, R is in 3NF.
• Every determinant (AB, BC, AC) is a candidate key. Hence, R is in BCNF as well.

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