Made Easy Mock

Question

Consider the following statements about relation R:

S1: If a relation R is in 3NF but not in BCNF, then relation R must consist proper subset of candidate key determines proper subset of some other candidate key.

S2: If a relation R is in 3NF but not BCNF, then relation R must consist atleast two over-lapped candidate keys.

Which of the following statements is/are correct?

(a) Both S1 and S2

(b) Only S1

© Only S2

(d) None of the above

Comments

S1 is right :3

not sure about S2 --> I think S2 is not true ..let me think more ....

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Magma

Why is S1 right?

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only S1 :3 ??

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if LHS is proper subset of candidate key, then isnt it violating 2NF? So it will be removed in 2 NF only right?

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Answer is Both are true

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R must consist proper subset of candidate key determines proper subset of some other candidate key.

A ----> B 

A is a proper subset of candidate key

B is a proper subset of candidate key

Partial ----> Partial

it's not BCNF but it's in 3NF  ?

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Answer is Both are true

-_- 

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Partial ----> Partial

ohh I overlooked this part :/ 

Ya so S1 is true. But S2?

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Both are true.

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Yup..got it :) thanks :)

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@Somoshree Datta 5

@Shubhanshu explain the 2nd statement ..I m not getting it!

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@himgta Consider Relation $R(A,B,C)$ with FD's $\{ C \rightarrow A , A \rightarrow C, BC \rightarrow D \}$ have overlapped CK $AB, BC$. Now apply $S_2$ you will find it true.

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@Shubhanshu

please give some example for s2 ?

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https://gateoverflow.in/218551/normal-forms?show=219407

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@garimanand check example in the comment.

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Thank you ,got it

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this is one example, but  in the S2 they have mentioned that it must have overlapped candidate keys. which i felt it need not be true because we can have so many example proving the S2 AS wrong.

eg:  R(ABCD)

AB->CD, C->B

in the given relation we don't need any overlapped keys but it is in 3NF but NOT IN BCNF.

correct me , if my approach towards the question is wrong.

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@ajay10 in your example we do have overlapped candidate keys those are $AB, AC$ where A is an overlapped prime attribute.

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thank you !  i got it ,i didn't overlook it carefully