GATE CSE 2002 | Question: 1.19

Question

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

• A. Zero
• B. More than zero but less than that of an equivalent $3NF$ decomposition
• C. Proportional to the size of F⁺ 
• D. Indeterminate

Comments

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

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@set2018

A table is in 4NF if it is in BCNF and it should not have any multivalued dependencies. Databases with multivalued dependencies exhibit redundancy.

So redundancy arising out of functional dependencies is 0 in BCNF but if the table has any multivalued dependencies then it has redundancy due to the multivalued dependencies.

See Ref: 1. https://en.wikipedia.org/wiki/Multivalued_dependency#Example
               2. https://www.studytonight.com/dbms/fourth-normal-form.php

Answer 1

Answer is A.

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:

• X → Y is a trivial functional dependency (Y ⊆ X)
• X is a super key for schema R
• http://en.wikipedia.org/wiki/Boyce%E2%80%93Codd_normal_form

Comments

(C) Proportional to the size of F+

I really didn't understand this option. What does it mean by the size of the F closure? 

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Yes, it's the size of closure.

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Jean no Multivalued Dependencies doesnt follow armstrong axioms like decomposition etc so they r NOT a type of FD

Answer 2

should be zero..
BCNF can have Multi valued dependency but no redundancy due to FDs..

Comments

1NF is atomic relation. I donot think attribute depends on it. Multivalued dependency is not in 1NF.

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@srestha

Thanks. I got it now. In 1NF we make attributes atomic, either by removing

• Composite attributes (by breaking them into simpler attributes), or,
• Multi-valued attributes (by making a new tuple for each 'value' in Multi-valued attribute)

Multi-valued Dependency is removed in 4NF.

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@srestha
In 4NF we remove the multivalued dependency. That means in BCNF multi-valued dependencies might be present. Because in 4NF, the table must be present in the form of BCNF. Correct me if I am wrong.

Answer 3

Yes , the answer should be zero. There should not be any redundancy due to FD in BCNF.

Comments

**redundancy.
There should not be any //dependency due to FD in BCNF.

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ohh yaa.. typos there.. correcting it..thanks :)

Answer 4

Explain please

BCNF can have Multi valued dependency but no redundancy due to FDs