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Which of the following statements is true?

$D_1$: The decomposition of the schema R(A, B, C) into R$_1$(A,B) and R$_2$(A,C) is always lossless

$D_2$: The decomposition of the schema R(A, B, C, D, E) having AD $\rightarrow$ B, C $\rightarrow$ DE, B $\rightarrow$ AE, and AE $\rightarrow$ C, into R$_1$(A,B, D) and R$_2$(A, C, C, D, E) is lossless

  1. Both $D_1$ and $D_2$
  2. Neither $D_1$ nor $D_2$
  3. Only $D_1$
  4. Only $D_2$
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3 Answers

Best answer
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Only D2. Since AD is key and it present in both the tables .

Not D1.

Since in D1 fd's not given...

If we take B -> A and C->A then it is lossy since no common attributes contain key from one of the table..
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For D1

It will be false becoz intersection of R1 with R2 wil A attribute which may be super key or which may not be super . So false

For D2

We have R1 itersection R2 as AD which is super key of R1 Relation so it will give lossless join decomposition

So D2 In only true

D option answer
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–1 votes
If we decompose a relation into two table where intersection of the two table is an attribute of the main table.For example:R1 intersection R2=A is an attribute of R.So,it is lossless.D1 is true.

D2 is obviously true.Using AD->B we can get whole attribute as AD is common in both table.So,D2 is lossless.

1)Both D1 and D2
Answer:

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