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Which one of the following statements about normal forms is $\text{FALSE}?$

1. $\text{BCNF}$ is stricter than $3NF$

2. Lossless, dependency-preserving decomposition into $3NF$ is always possible

3. Lossless, dependency-preserving decomposition into $\text{BCNF}$ is always possible

4. Any relation with two attributes is in $\text{BCNF}$

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option $C$
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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)

but, option (c) is about BCNF, which is not true always in case of BCNF
How option D is true?