we are in 1NF if we don't have a non-atomic domains in our relation.

we are in BCNF if we don't have a functional dependency on the left hand side that is not a superkey.

as far as i know BCNF definition isn't concerned whether a relation has a non-atomic domains or not.

so i assume that not all BCNF schemes are in 1NF, and not all 1NF schemes are in BCNF.

i ask that question because i saw the following picture.

from the picture it looks like BCNF is subset of 3NF which is subset of 2NF which is subset of 1NF.

therefore it's the most restrictive.

so from that picture i kinda assume that BCNF schemes cannot have a non-atomic values.

but from where i read it, the definition never mentioned something about atomicity in BCNF.

CodePudding user response：

1NF is not considered a normal form as the others, since nowadays it is considered implicit to the relational data model. In other worlds, if a table is not in 1NF, it is not a relation, while all the “other” normal forms are defined only for relations. So, obviously, any normal form from the second one, implicitly implies the so-called First Normal Form.