#normalisation #dbms

Question

Q: What is the highest normal form of a relation R(A, B, C, D, E) with FD set?

{B → A, A → C, BC → D, AC→ BE}

 Options:

1. 2NF

2. 3NF

3. BCNF

4. 4NF

Answer 1

Candidate keys for the relation R are A,B. So, prime attributes: A,B and non prime attrubutes are C,D,E.

LHS of every dependency is a super key. So, R is in BCNF.

 

Comments

Why not it is 4NF as it is also satisfying the requirements of 4 NF

Because there are no non‐trivial multi‑valued dependencies given, RR not only satisfies BCNF but trivially meets the requirements for 4NF as well (4NF simply adds the rule “no non‑trivial MVDs unless the left side is a superkey”).

• BCNF: All FDs X→YX→Y have XX a superkey.

• 4NF: All non‑trivial MVDs X↠YX↠Y have XX a superkey.

Since our dependency set only involves FDs and we’ve shown every FD has a superkey on the left, we’re in BCNF—and with no MVDs to violate 4NF, we’re also automatically in 4NF.

So yes, RR is in 4NF (and BCNF), but when the question is framed purely around FDs, the “highest” normal form you normally cite is BCNF.