Which normal form is the highest that satisfies the functional dependencies(DBMS)?

Let's take the dependencies F= {AB->CDEF, AF->ED, F->B} which ONE of the following is the highest normal form that a table R=ABCDEF could satisfy.

Select any one from the following −

  • No normal form would be satisfied.
  • Boyce-Codd Normal Form
  • 1st Normal Form
  • 2nd Normal Form
  • 3rd Normal Form

Given Functional dependencies of F are as follows −

AB ---> CDEF

AF ---> ED

F ---> B

Now in R.H.S (Right Hand Side) of Functional dependencies of F, attributes B,C,D,E,F are all present but attribute A is missing. So, attribute A must be the part of Super Key.

We have to find the closure of A (A+),

A+ = A only, So attribute A alone can't be the key. Thus we have to combine A with other attributes of F and then find candidate keys of F.

Find the Candidate Keys of F


AC+ = AC

AD+ = AD

AE+ = AE


Now since closure of (AC, AD, AE) is not covering all the attributes of F. So again, we have to combine AC, AD, AE to check whether their combinations become a candidate key of F or not.





So finally, we are confirmed that AB and AF are the only candidate keys of F as their closure is covering all the attributes of F.

So prime attributes of F are A, B, F and non-prime attributes of F are C, D, E.

Check for Highest Normal Form (NF)

We will start from highest normal forms in which BCNF form is the highest normal form and if F is in BCNF normal form then it will also be under 1NF, 2NF and 3NF.

Check For BCNF

All functional dependencies of F X ---> Y, where all X must be the super key.

Out of all functional decencies of F below, only AF and AB are the super keys but F is not a super key.

(AB ---> CDE, AF ---> ED, F ---> B)

So F is not in BCNF as all X of (X ---> Y) are not super keys.

Check for 3NF

For F to be in 3NF there shouldn't be an occurrence of transitive functional dependency for non prime attributes or say no non-prime attributes in F should derive to other non-prime attributes.

And in F (X --> Y) All X of Functional dependency are prime attributes as AF, AB are super keys and F is a prime attribute. So, no occurrence of transitive dependency and thus it is in 3NF.

And F is also in 2NF as no partial dependencies are there, i.e. no part of candidate keys are deriving to any non-prime attributes.

If F is in 3NF then it is also in 2NF and 1NF. As 3NF is the highest Normal Form out of them.


The table R(A,B,C,D,E) satisfies 3NF.