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Relation $R$ with an associated set of functional dependencies, $F$, is decomposed into $\text{BCNF}$. The redundancy (arising out of functional dependencies) in the resulting set of relations is

1. Zero
2. More than zero but less than that of an equivalent $3NF$ decomposition
3. Proportional to the size of F
4. Indeterminate
edited | 2.8k views
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Question is 19?
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Yes, thanks for catching it.  It has been corrected. You can solve it now. :-)
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typo in F*

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corrected :)
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which book?
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this is a error i have confirmed from vani institute's teacher .this was there in there study material.
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Any good references to study MVDs?
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based on  functional dependency BCNF has 0 percent redundancy ,but is there any chance for other type redundancy m not getting other type ?explain pls

If a relation schema is in BCNF then all redundancy based on functional dependency has been removed, although other types of redundancy may still exist. A relational schema R is in Boyce–Codd normal form if and only if for every one of its dependencies X → Y, at least one of the following conditions hold:

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question is redundancy (arising out of functional dependencies) in the resulting set of relations is ?

there is no redundancy due to FDs.
Should be A ??
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Yes .ans is A
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please give an example where redundancy due to functional dependencies exist. ?
I am not getting what is diff between redundancy due to functional dependency and due to other reasons..

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if BCNF has multivalued dependencies..then redundancy will happen? right..?
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Relation that have redundant data problem called anomalies. Anomalies can only removed by normalization.

1st NF talks about atomic values and non-repeating groups.
2nd NF enforces that a non-Key attribute should belong to entire Key attribute.
3rd NF makes sure that there should be no transitive dependency between a non-Key and a Key attribute.

and

Redundancy allowed by 3NF is disallowed by BCNF

BCNF is stricter than 3NF 3NF is stricter than 2NF

should be zero..
BCNF can have Multi valued dependency but no redundancy due to FDs..
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@digvijay pandey can you please explain what is multi valued dependency? And how it can be present in BCNF?
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Hello hemant

A relation would be BCNF when functional dependencies are like $x->y$ ; where x is super key and in that way when attributes are dependent on super key , redundancy can't exist.

But what will happen when we have such a relation that doesn't contain any non-trivial functional dependency?Hope you can guess that in such case super key will be the whole set of attributes.So eventually we can say such a relation will be BCNF relation. Can we say that this kind of relation will be free of redundancies ? There comes the term call 'Multivalued dependency', whose presence make the relation redundant. like

R(course_id,professor_name,Books_name)

 Course_id Professor_name Books_name C1 P1/P2 B1/B2/B3 C2 P2/P3 B4/B5 C3 P4 B4

You can see , this relation is in BCNF as no functional dependencies exist there.

But here exists multivalued dependencies (basically multivalued dependency means multiple values of some attributes are dependent on some attribute value )

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Yes , the answer should be zero. There should not be any redundancy due to FD in BCNF.
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**redundancy.
There should not be any //dependency due to FD in BCNF.
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ohh yaa.. typos there.. correcting it..thanks :)
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in above question, I don't understand the meaning of ( arising out of functional dependencies ) I am thinking like "arising out of" mean, not due to functional dependencies and you all explained that it due to functional dependencies how to get it please help ?
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there can be other forms of dependency too, apart from FD. In BCNF, FDs are preserved.
Increasing order of redundancy:

4NF < BCNF < 3NF < 2NF < 1NF < un-normalized

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This should be 0. Ans -> A
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Yes Answer is b because there can be redundancy beacuse of MVDS
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@Akash please share us link if you have any, how 3NF redundancy became zero.
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@ Akash Kanase b is right