Consider the following statements regarding database normal forms: 1. Any relation with two attributes is BCNF. 2. Lossless, dependency - preserving decomposition into BCNF is always possible. 3. Lossless, dependency - preserving decomposition into 3NF is always possible. 4. BCNF is stricter than 3NF. Which of the above statements are correct?

Option 2 : 1, 3 and 4

Statement 1: Correct

Any relation with two attributes will always in BCNF

Example:

Relation R = {x, y} non trivial FD’s of this relation is x - > y and y - > x and these both FD’s are in BCNF so this statement is true.

Statement 2: Incorrect

 It is not always possible to decompose a table in BCNF and preserve FD’s and lossless decomposition will always be possible in BCNF.

Example:

XY - > Z and Z - > Y cannot be decomposed in BCNF

Statement 3: Correct

Lossless, dependency - preserving decomposition into 3NF is always possible this statement is true.

Statement 4: correct

BCNF is stricter form of normalization than 3NF because it eliminates the second condition of 3NF.