Question

Q3: Given a relational schema R = {A,B,C,D,E,F,G,H,1,J,K} and a set of functional dependencies F {A B C D E, E F G H I J,AI →K} and a key(R) = AI = 1. Is R in BCNF? If yes, justify your answer [5 points] 2. If no, explain why and decompose R for two levels only [10 points] 3. Check whether the decomposition in step 2 dependency preserved or not [5 points]

Answer 1

R = SA B C D E F G H I J K3 F- A+BCDEF E + FGHI, IAJ, AI+k} To check a in BCNF If and If determinant A Relation R is in BCNF, only Х у e superkey is super key. not ABCD EF GH voilates , at- Et F G H Condition for BONF [A is super key } [E is not super key] [I ūs not super ky ] is super key It IJ AIKBCDEFGH Ait [A1 - R is not in BCNF R into of two level 2 Now, Decompose R R Rg Rg = SAJIKS R, - SABCDEFGH3

3 cheeking for Decomposition in whether it is Dependency preserving :- To check, map. all the Dependency to becomposed Relation that is R, 8 de , if all dependency mapped and no left then se composed Dependency pre serving one out then Relation R, 8 R2 are R, - {ABCDEFGH 3 Rg = { AJIK 3 A + BCDE I+J AITK Et FGH & All dependency matched, Hence Relation a is Dependency preserved.
to check a relation, whether it is in bcnf or not, check all the determinent of the dependency, if all the determinent are superkeys (deriving all attributes of relation) then its in bcnf otherwise not.