Re: ?? Functional Dependency Question ??

tlbaxter99_at_yahoo.com wrote:

> Hi all,
>
> I'm reading Elmasri & Navathe's "Fundamentals of Database Systems, 4th
> ed.". The authors discuss how, given a set if FDs, additional FDs can
> be inferred. The authors provide six "Inference Rules". At one point
> the authors say this:
>
> "Although X->A and X->B implies X->AB by the union rule stated above,
> X->A, and Y->B does *not* imply that XY->AB."
>
> I'm not seeing this. It seems to me that X->A, and Y->B *DOES* imply
> that XY->AB.
>
> I'm sure I'm wrong but I'm not seeing it. Can someone explain?
>
> Thanks

I'm not seeing it either. By these truth tables, it seems to:

XY AB X->A Y->B (X->A)(Y->B) XY->AB (X->A)(Y->B)->(XY->AB)

00  00  1     1          1         1                 1
00  01  1     1          1         1                 1
00  11  1     1          1         1                 1
00  10  1     1          1         1                 1
01  10  1     0          0         1                 1
01  11  1     1          1         1                 1
01  01  1     1          1         1                 1
01  00  1     0          0         1                 1
11  00  0     0          0         0                 1
11  01  0     1          0         0                 1
11  11  1     1          1         1                 1
11  10  1     0          0         0                 1
10  10  1     1          1         1                 1
10  11  1     1          1         1                 1
10  01  0     1          0         1                 1
10  00  0     1          0         1                 1

(View with a fixed width font)

Can anyone find a mistake in the above truth tables? Is there a difference between functional dependency and implication that I need to learn? Received on Sat Oct 18 2008 - 10:18:16 CDT