Given R(ABCDEFG) and functional dependencies
AB $\rightarrow$ C
BC $\rightarrow$ A
AC $\rightarrow$ B
B $\rightarrow$ D
D $\rightarrow$ E
Decompositions:
1. R1(ABC) R2(ABFG) R3(BD) R4(DE)
2. R1(ABC) R2(BCFG) R3(BD) R4(DE)
3. R1(ABC) R2(ACFG) R3(BD) R4(DE)
Is all of these decompositions are lossless, dependency persevering and BCNF?
Please confirm. Thank you.