Re: circular relationships ok?


Brian Selzer wrote:
"vc" <boston103@xxxxxxxxxxx> wrote in message
news:1141397694.943802.23190@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

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.

.

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