Give an example of relation which is in 3 normal form but not in BCNF

# Give an example of relation which is in 3 normal form but not in BCNF

if the candidate keys in a 3NF relation are

all atomic, or

non-atomic but non-overlapping,

it is guaranteed that the relation is in BCNF.

The simplest relation which violates BCNF but meets 3NF can be defined as below

A,B -> C C -> B

In this case, candidate keys are (A,B) and (A,C).

It meets 3NF because

the right-hand-side of all functional dependencies is a primary attribute.

It violates BCNF because

C -> B, but the left-hand-side is not a superkey.