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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 #

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 .
Union is done on the dependencies and not on the decomposed relations as per the given question.
Yes that is correct. Actually I thought closure is what the question implied.

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

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.