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1 vote
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Consider a relation schema r(A,B,C,D) with F as set of functional dependencies. F contain following functional dependencies:

A -> B

A -> D

A -> C

B -> D

we decompose the relation r into two relation schemas r1(A,B,C) and r2(B,D). The statement

(Functional dependency in r1) U (Functional dependency in r2) = F is correct ?

#dbms #
in Databases edited by
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4 Comments

What’s your answer?
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Sir , This ques was given in madeeasy testseries and this was one of the option and they were given that it's not correct but according to me it is correct becoz ...

R1(A,B,C)

A->B

A->C

R2(B,D)

B->D

and union of both R1 and R2 will derive A->D also so every dependency which is in given Relation is derived through union so the union must be equivalent to F ...i am thinking like this Sir ...correct me if I am wrong Sir .
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Union is done on the dependencies and not on the decomposed relations as per the given question.
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Yes that is correct. Actually I thought closure is what the question implied.
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1 Answer

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yes it is correct, since A -> B and B -> D gives A -> D by transitive property of armstrong axioms

3 Comments

That’s true when you talk about dependency preserveness. But how can you apply transitive rule when talking about mere sets?
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Since $F_{R_{1}} ∪ F_{R_{2}}$ has both A -> B and B -> D, hence i think we can apply the  transitivity rule and derive A -> D.
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No. When doing union operation on sets we don't apply transitivity rule. That's why for functional dependency closure operation is there.
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