GATE CSE 2002 | Question: 16

Question

For relation R=(L, M, N, O, P), the following dependencies hold:

$ M \rightarrow O,$ $NO \rightarrow P,$ $P \rightarrow L$ and $L \rightarrow MN$

R is decomposed into R₁ = (L, M, N, P) and R₂ = (M, O).

• A. Is the above decomposition a lossless-join decomposition? Explain.
• B. Is the above decomposition dependency-preserving? If not, list all the dependencies that are not preserved.
• C. What is the highest normal form satisfied by the above decomposition?

Answer 1

Those who solving the Part A Refer this link . 

Here There is also second method must to check, 

When You apply the  first method of Lossless join 

1. R1 intersection R2 →  R1 or R2 must have superkey( then it lossless join 

        If not then check for this also ,

2. if (R₁ ∩ R₂)→ (R₁ - R₂) or (R₁ ∩ R₂)→ (R₂ - R₁) holds in F⁺(this should be present in the given Functional Dependencies)  then it’s a lossless-join decomposition

database - Lossless Join Decomposition - Stack Overflow