virtual gate

Question

Relation R(ABCDEF) with the following set of functional dependencies {AB→CDEF, C→A, D→B, E→F, B→E}.

The decomposed relationslations of R into 3NF are __________________________.

Comments

Can we apply 3nf Synthesis Algorithm....Please solve through this ... I can't able to get the same result.

Answer 1

answer is B)

among all fd ...candidate keys are AB,CD,CB,AD...hence prime attributes are (A,B,C,D)

now look out for FD ...the one which breaks 3nf rule will be split as table.....

AB->CDEF......(left side is superkey ..so left it as it is)

C->A  in 3nf as right side is prime attribute...

D->B in 3nf as B is prime attribute.

B->E breaks 3nf ...so take closure of B....

(B)^+=BEF....

but again E->F breaks 3nf so separate it ....hence tables will be BE and EF.....now to have lossless decomposition remaining attributes of table are kept in one more table......

remaining are A,B,C,D......

hence we have 3 tables ABCD,EF,BE..

Answer 2

option b