Re: circular relationships ok?

Brian Selzer wrote:
> "vc" <boston103_at_hotmail.com> wrote in message
> news:1141397694.943802.23190_at_t39g2000cwt.googlegroups.com...
> >
> > Brian Selzer wrote:
> >>[...]
> >> if a and b are values
> >> for A and B respectively in a tuple of R, a implies b and b implies a,
> >> therefore, a iff b.
> >
> > That does not make any obvious sense. What do you mean by '[value] a
> > implies [value] b' ? Are you considering only the Boolean domain ?
> >
>
> A key is a set of attribute values, or facts. A set of facts is a
> proposition in conjuctive normal form.

It's not, but let's pass on it.

>Therefore, a functional dependency
> is essentially a logical implication. For example, assume that a tuple in a
> relation with the attributes A, B, and C has values a, b, and c
> respectively. Then the following statements are true: A has value a. B has
> value b. C has value c. If {A, B} is a candidate key, then the statement "A
> has value a, and B has value b." implies the statement "C has value c."
> because by definition, the value of a candidate key determines all other
> values in a tuple.

So what you are trying to say is that since, e.g., X=10 and Y=10, we can write (X=10) <--> (Y=10). So why do you use the fancy notation to express such trivial idea ?

Now, with your three relations R, S, T you have six sets representing columns A, B, C:

Ar, Br, As, Bs, At, Bt.

So while it's true that, say, As=Bs, it's not generally true that Br=Bs unless you stipulate so. Therefore,

"Consequently, a iff b iff c."

still does not make any obvious sense. Received on Sat Mar 04 2006 - 15:24:43 CET