Which one of the following statements about normal forms is $\text{FALSE}?$
$\text{BCNF}$ is stricter than $3NF$
Lossless, dependency-preserving decomposition into $3NF$ is always possible
Lossless, dependency-preserving decomposition into $\text{BCNF}$ is always possible
Any relation with two attributes is in $\text{BCNF}$
why dependency preserving decomposition into 3NF is always possible?
I found that indeed it is true that a dependency preserving, lossless join decomposition into 3NF is always possible. here is link. (2nd point)
For option D-https://gateoverflow.in/1797/gate2014-1-30
As the FALSE statement is asked, therefore, Option C
It is not always possible to have a dependency preserving BCNF decomposition.
For example. this 3NF relation cant be transformed into BCNF
AB –> C, C –> B
Regarding other options, it is always possible to have a 3NF or lesser normalization to be lossless and dependency preserving.
If relation is in 3NF then both lossless and dependency preserving are Guaranteed
and If relation is in BCNF lossless is Guaranteed but dependency preserving is Not Guaranteed.
So, clearly option (C) is false.