Test by Bikram | Databases | Test 1 | Question: 18

Question

$R (A,B,C,D)$ is a relation. Which of the following does not have a lossless join dependency preserving BCNF decomposition

• A. $A \rightarrow B, \ B \rightarrow CD$
• B. $A \rightarrow B, \ B \rightarrow C, \ C \rightarrow D$
• C. $AB \rightarrow C,\  C \rightarrow AD$
• D. $A \rightarrow BCD$

Comments

without decomposed relations given, how can we assume that which decomposition will be preserving decompo? and even in blind case we can say that option D always preserves dependency as it is in original form, no more than one relation in decomposition than how it could not preserve lossless join dependency?

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We have to see if a possible decomposition is there - and yes, answer is C and not D.

https://gateoverflow.in/741/gate2001-2-23

Answer 1

All are dependency preserving and lossless.

But in Option C

{A,B} is the only candidate key, hence A and B are prime attributes.

$C\rightarrow AD$ would be illegal as C isn't a superkey. Hence Option C won't be BCNF.