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Phil Cook wrote:
> I am told that if X ---> Y and YW ---> Z, then XW ---> Z
>
>
> Given schema(R) = {C,T,H,R,S,G}, I have the following FDs:
>
> HS ---> R
> HR ---> C
>
> Can I therefore say that HHS ---> C and from that HS ---> C?
Yes, you can either show this with Armstrong's rules or computing the closure of HS. With Armstrong's rules the proof goes like this:
(1) HS -> R (axiom 1) (2) HS -> HR (extension rule: X->Y => XZ->YZ) (3) HR -> C (aziom 2) (4) HS -> C (transitivity rule for (2) and (3))
When you compute the closure you get the following:
HS -> HS (initialization step) HS -> HSR (apply first rule) HS -> HSRC (apply second rule)
Since C is in the set on the right hand side it follows that HS -> C.
Kind regards,
-- Jan HiddersReceived on Mon Apr 02 2001 - 03:37:13 CDT