##
**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?*
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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