DM: Functional Dependency

[Michael Walther]

>Hello,

> I have a question regarding functional dependency. I have a table 
>with say 4 attributes, A, B, C, D. Now after processing through the 
>> 
table I  have found that the following functional dependencies hold 
>good on the  table:

>       A->B, A->D, B->C, D->A, D->B, D->C.

> Now my question is that from this set of functional dependencies can
> I say that the following also holds good:

>  A->BD, D->ABC   -  (Is this also true)
>  and is
>  AC->BD true.

> Thanks for the answer, Regards
> -Srikanth
                                                
IF X -> Y stands for := there is a function f:X->Y
(For ervery x from X there is exact one y from Y , for all x from X) 
and XY is the crossproductfrom X and Y, then
from f:A-> B and g:A->D you can define a function  h:A -> (B,D)
with h(a)=(f(a),g(a)), hence A-> BD.
You also conclude D->A, D->B, D->C then  D->ABC 
and A->B, A->D then AC->BD , 
cause you may just drop C.
h':AC -> BD is just h'(a,c) := h(a) hence 
from A->B, A->D follows AC->BD.
 regards
 Michael Walther
 mail : 100721,15
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