boyce-codd normal form

boyce-codd normal form (BCNF): was proposed as a simpler form of 3NF, but it was found to be stricter than 3NF. that is, every relation in BCNF is also in 3NF; however, a relation in 3NF is not necessarily in BCNF.

a relation schema $\text{[math]}$ is in BCNF if whenever a nontrivial functional dependency $\text{[math]}$ holds in $\text{[math]}$ , then $\text{[math]}$ is a superkey of $\text{[math]}$ .
[cite:;from @elmasri_db_2015 chapter 14.5 boyce-codd normal form]

[cite:;see @elmasri_db_2015 chapter 14 basics of functional dependencies and normalization for relational databases]

a relation satisfies the BC/NF normal form if:

it satisfies the 3nf normal form;
if there exists a functional dependency $\text{[math]}$ , then $\text{[math]}$ is the key of the relation. i.e. there exist no dependencies $\text{[math]}$ such that $\text{[math]}$ isnt in the key or is only part of the key.

the normalization process of bcnf is as follows: in the case that such a dependency $\text{[math]}$ exists, create a new relation where $\text{[math]}$ is the key.

a student can take many courses and the converse is true, when a student takes a course a single person lectures them, a course can be given by different lecturers, but a lecturer can only teach one course
given the following relation: (_student id, course_, lecturer id)
this relation doesnt satisfy BCNF because we have the relation lecturer id $\to$ course. to fix that we create a new relation (course, _lecturer id_)