database normalization - BCNF decomposition that results in different decompositions (both faithful or faithless)? -

database normalization - BCNF decomposition that results in different decompositions (both faithful or faithless)? -

this question 19.10 (4) in textbook database management systems raghu ramakrishnan, johannes gehrke (in case anyone's curious - reply not included of course, why needed ask)

and noticed there 2 ways create bcnf decomposition:

we're given r = abcd , functional dependencies: -> b, b -> c, c -> d

key: can decompose bcnf either using b -> c or c -> d @ start

if decompose along b -> c @ start, r1 = ab , r2 = bc , r3 = bd (this not faithful) if decompose along c ->d @ start, r1 = ab, r2 = bc , r3 = cd (this faithful)

i'm quite new doing bcnf decomposition, correct? it's possible have multiple different bcnf decompositions depending on chosen starting fd?

thanks in advance :)

database-normalization bcnf