Normalization-(prime attribute -> prime attribute dependency is there in BCNF)

Question

$AB\rightarrow CD$

$CD\rightarrow AB$

$A\rightarrow C$

Is it in 3NF or BCNF?

Is prime attribute -> prime attribute dependency is there in BCNF?

Comments

It is in 3NF. BCNF requires LHS of each FD to be a super key.

Answer 1

Since No Non-Prime Attribute is there, the Relation is definitely  in 3NF But  NOT in BCNF Because "For a Relation to be in BCNF, ALL the Non-Trivial FD's $X \rightarrow Y$  have to have $X$ as Super Key. If a Proper Subset of Candidate key is deriving another Proper Subset of a Candidate key, then the Relation is Not in BCNF.

Answering Your Doubt, $Prime\, \, Attribute \rightarrow Prime\, \, Attribute$ dependency Should Not be there in the relation Unless that Prime attribute itself is Candidate key or Super key. The "Prime attribute" term  doesn't give clear idea about it and that's why "Proper Subset of Candidate Key" Terminology is used. (Of course, Proper Subset of Candidate key is set of Prime attribute(s) only, But it cannot be Candidate key itself Whereas Prime attribute could mean Candidate key too, depends on context)