GO Classes DPP | GATE CS, DA | DBMS | Decomposition

Answer 1

First check whether all attributes are preserved.

$R_1\cup R_2$

$=\{A,B,C\}\cup\{D,E,F\}$

$=\{A,B,C,D,E,F\}$

Therefore, no attribute has been lost. It is a valid decomposition.

Now check the FDs.

Inside $R_1$, we can enforce

$A\to B$ and $A\to C$.

Inside $R_2$, we can enforce

$F\to D$ and $F\to E$.

Therefore, all the original dependencies can be checked in the decomposed relations.

So the decomposition is dependency preserving.

However,

$R_1\cap R_2=\varnothing$

There is no common joining attribute.

Their natural join therefore behaves like a Cartesian product.

For general valid instances, this may create combinations that were not present in the original relation.

These extra combinations are spurious tuples.

Therefore, the decomposition is not lossless.

Hence, the decomposition is dependency preserving but lossy.

The correct answer is B

Answer 2

it is not lossless becoz we do not have common attribute in R1 and R2 .

it is dependency preserving bcz A->B,A->C can be derived from R1 and F->D,F->E can be derived from R2
 

So ans is B