Self Doubt

Question

3NF Decomposition for the relation R(A,B,C):

A $\rightarrow$ BC

B $\rightarrow$ C

such that it is lossless and dependency preserving.

 

[It is said that 3NF decomposition is possible for any relation but I couldn't find decomposition for the above]

Comments

Dependency preserving means F$^{+}$ = F1$^{+}$ U F2$^{+}$ U F3$^{+}$ U ...

In our case,

LHS: {A->B, A->C, B->C}

RHS: {A->B, B->C}

Clearly, LHS not equal to RHS. So how dependency preserving?

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so A->C is not in RHS? look at the closure of A

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Oh yess.

Dependency preserving means F$^{+}$ = (F1$^{+}$ U F2$^{+}$ U F3$^{+}$ U ...)$^{+}$

So A->C  holds by transitivity.

Thanks