Re: armstrong's axioms: augmentation - help pls

From: pc <>
Date: Thu, 02 Dec 2004 15:10:04 GMT
Message-ID: <gfGrd.224517$df2.196441_at_edtnps89>

loveboat wrote:

> hi,
> in armstrongs axioms, i don't get the augmentation, which is:
> (X -> Y) => (XZ -> YZ)

I don't know if you find this any easier to follow than I do, but here is a proof from one of CJ Date's books. It is a proof by contradiction. (I have changed his attribute names A, B, and C to your X, Y and Z respectively):

"Let X->Y. Then, whenever two rows r1 and r2 agree on X, they also agree on Y.
Suppose r1 and r2 agree on XZ but not on YZ. Since r1 and r2 obviously agree on Z, they must therefore disagree on Y. But this is a contradiction, since r1 and r2 agree on XZ and hence on X, and X->Y.
Hence AC->BC"

pc Received on Thu Dec 02 2004 - 16:10:04 CET

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