ACE volume 1 DBMS

Question

Suppose the  functional dependencies B--->C

holds in a relation R(A,B,C,D).which additional FD will make R be in 3NF ,but not in BCNF?

a)D--->AB        b)AC--->D

c)CD-->B         d)AD--->B

Answer 1

Check one by one...

option A:-  D->AB

Now My Functional Dependency set is {B->C and D->AB} therefore D is the Key for the relation, now B->C leads to non-prime transitivity, therefore It is not in 3NF

 

option B:-  AC->D

Now My Functional Dependency set is {B->C and AC->D} therefore AB is the Key for the relation, now B->C leads to partial functional dependency, therefore It is not in 2NF ===> It is not in 3NF

 

option C:-  CD->B

Now My Functional Dependency set is {B->C and CD->B} therefore ABD or ACD are the Keys for the relation, now B->C leads to prime transitivity, therefore It is not in BCNF but It can in 3NF

 

option D:-  AD->B

Now My Functional Dependency set is {B->C and AD->B} therefore AD is the Key for the relation, now B->C leads to non-prime transitivity, therefore It is not in 3NF.

 

Option C is correct