Functional preserving

Question

Given $R(A,B,C,D,E)$ and $F:\left \{A\rightarrow BC ,CD\rightarrow E,B\rightarrow D,E\rightarrow A\right \}$,Decompose into $BCNF?$

$(a)$Every $BCNF$ is $3NF$ and vice versa $?$

$(b)FD$ preserving or not$?$

$(c)$ Lossless decomposition or lossy  decomposition?

Comments

I have the only problem, how to decompose the relation?

can you show, how to decompose?

Answer 1

We have to decompose it for the functional dependency that doesnot satisfy the BCNF condition.out of all the given functional dependencies the property of BCNF that the left hand side should be a super key is satisfied by all the functional dependencies but not by B implies D as B is not a super key. So in order to make it IN BCNF form we need to decompose it into 2 relations such that these  conditions are satisfied, so we break it up intp BD and ABCE. Here for BD relation B->D holds and B is a superkey so BCNF(every relation with two attributes is in BCNF) and similarly ABCE also satisfies the properties of BCNF but  all fds are not preserved.

Comments

ma'am, my decomposition is right and FD is not preserved and it is lossless BCNF.

please check it

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@Lakshman decomposition has some procedure to follow

So, plz check more question on this

chk this https://gateoverflow.in/79463/decomposition

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Ok ma'am thank you