How I reduced to BCNF for this question, Could you please help me have a check,
R(A, B, C, D, E)
FDs: A --> B, D --> E, C--> D
Reduced to BCNF:
R1(A,B), R2(D, E), R3(C,D)
I am not sure about my work. Thanks
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I think you've lost information that adding R4(A,C) would preserve.
The original relation records that an A value, a B value, a C value, a D value and an E value are all associated with each other. The FDs explain how some of the values can be determined by (from) others. For example, if you know the D value, you know what the E value must be.
Your revised schema preserves all the information except that a specific A value is associated with a specific C value. Adding R4(A,C) preserves that information.