Question

Consider the following statements given below:

$S_1$: There is always possible a lossless, dependency preserving BCNF decomposition.

$S_2$: Any relation with two attributes is in BCNF.

$S_3$: For two relation R(A, B) with functional dependency F = {A $\to$ B} and S(B, C) with functional dependency $F=\{B\to C\}$, natural join of R $▹◃$ S is in BCNF.

Which of the following statements are true?

• A. $S_{1}and{S}_2$ only
• B. $S_{2}and{S}_3$ only
• C. $S_1,S_{2}and{S}_3$
• D. Non of the above

Answer 1

The correct option is D Non of the above

$S_1$: Lossless dependency preserving BCNF decomposition is not always possible. $S_1$ false

$S_2$: With two attribute a relation is always in BCNF. $S_2$ true

R (A , B)

$A\to B,B\to A$

Both A and B are key for R.

$S_3$: The natural join of R and S will have functional dependencies $A\to B$ and $B\to C$, Which is not in BCNF, $S_3$ false

So option (d) is correct.