Decompose below relation into 2NF,3NF and BCNF with lossless join and Dependency Preserving.
$R(ABCDE)$
$F=\{AB\rightarrow C,DE \rightarrow C,B \rightarrow D\}$
According to my analysis
The only key here is $ABE$
So, Dependencies $AB\rightarrow C,B\rightarrow D$ are partial dependencies.
I decomposed as below
$R_1(ABC) \{AB\rightarrow C\}$
$R_2(BD)\{B \rightarrow D\}$
$R_3(CDE) \{DE \rightarrow C\}$
And All three above are in BCNF as well.
Is my decomposition correct?