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Re: Pseudo transitivity

From: Jan Hidders <hidders_at_REMOVE.THIS.win.tue.nl>
Date: 2 Apr 2001 08:37:13 GMT
Message-ID: <9a9dnp$5vs$1@news.tue.nl>

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 Hidders
Received on Mon Apr 02 2001 - 03:37:13 CDT

Original text of this message

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