Mark Forums Read

?? Functional Dependency Question ??

Go Back

comp.databases.theory comp.databases.theory

Reply

Page 3 of 35

3

#21

Old

paul c

Posts: n/a

Re: ?? Functional Dependency Question ?? - 10-18-2008 , 10:36 AM

tlbaxter99 (AT) yahoo (DOT) com wrote:

Quote:

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

Here's what I get using Armstrong's Axioms:

i) X -> A (given)
ii) XY -> AY (augment i) with Y)

iii) Y -> B (given)
iv) AY -> AB (augment iii) with A )

v) XY -> AB (ii), iv), transitivity)

Maybe the book has a typo? If so, I wonder what they meant to say?

Reply With Quote

#22

Old

paul c

Posts: n/a

Re: ?? Functional Dependency Question ?? - 10-18-2008 , 10:36 AM

tlbaxter99 (AT) yahoo (DOT) com wrote:

Quote:

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

Here's what I get using Armstrong's Axioms:

i) X -> A (given)
ii) XY -> AY (augment i) with Y)

iii) Y -> B (given)
iv) AY -> AB (augment iii) with A )

v) XY -> AB (ii), iv), transitivity)

Maybe the book has a typo? If so, I wonder what they meant to say?

Reply With Quote

#23

Old

paul c

Posts: n/a

Re: ?? Functional Dependency Question ?? - 10-18-2008 , 10:36 AM

tlbaxter99 (AT) yahoo (DOT) com wrote:

Quote:

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

Here's what I get using Armstrong's Axioms:

i) X -> A (given)
ii) XY -> AY (augment i) with Y)

iii) Y -> B (given)
iv) AY -> AB (augment iii) with A )

v) XY -> AB (ii), iv), transitivity)

Maybe the book has a typo? If so, I wonder what they meant to say?

Reply With Quote

#24

Old

paul c

Posts: n/a

Re: ?? Functional Dependency Question ?? - 10-18-2008 , 10:36 AM

tlbaxter99 (AT) yahoo (DOT) com wrote:

Quote:

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

Here's what I get using Armstrong's Axioms:

i) X -> A (given)
ii) XY -> AY (augment i) with Y)

iii) Y -> B (given)
iv) AY -> AB (augment iii) with A )

v) XY -> AB (ii), iv), transitivity)

Maybe the book has a typo? If so, I wonder what they meant to say?

Reply With Quote

#25

Old

paul c

Posts: n/a

Re: ?? Functional Dependency Question ?? - 10-18-2008 , 10:36 AM

tlbaxter99 (AT) yahoo (DOT) com wrote:

Quote:

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

Here's what I get using Armstrong's Axioms:

i) X -> A (given)
ii) XY -> AY (augment i) with Y)

iii) Y -> B (given)
iv) AY -> AB (augment iii) with A )

v) XY -> AB (ii), iv), transitivity)

Maybe the book has a typo? If so, I wonder what they meant to say?

Reply With Quote

#26

Old

paul c

Posts: n/a

Re: ?? Functional Dependency Question ?? - 10-18-2008 , 10:36 AM

tlbaxter99 (AT) yahoo (DOT) com wrote:

Quote:

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

Here's what I get using Armstrong's Axioms:

i) X -> A (given)
ii) XY -> AY (augment i) with Y)

iii) Y -> B (given)
iv) AY -> AB (augment iii) with A )

v) XY -> AB (ii), iv), transitivity)

Maybe the book has a typo? If so, I wonder what they meant to say?

Reply With Quote

#27

Old

paul c

Posts: n/a

Re: ?? Functional Dependency Question ?? - 10-18-2008 , 10:36 AM

tlbaxter99 (AT) yahoo (DOT) com wrote:

Quote:

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

Here's what I get using Armstrong's Axioms:

i) X -> A (given)
ii) XY -> AY (augment i) with Y)

iii) Y -> B (given)
iv) AY -> AB (augment iii) with A )

v) XY -> AB (ii), iv), transitivity)

Maybe the book has a typo? If so, I wonder what they meant to say?

Reply With Quote

#28

Old

paul c

Posts: n/a

Re: ?? Functional Dependency Question ?? - 10-18-2008 , 10:36 AM

tlbaxter99 (AT) yahoo (DOT) com wrote:

Quote:

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

Here's what I get using Armstrong's Axioms:

i) X -> A (given)
ii) XY -> AY (augment i) with Y)

iii) Y -> B (given)
iv) AY -> AB (augment iii) with A )

v) XY -> AB (ii), iv), transitivity)

Maybe the book has a typo? If so, I wonder what they meant to say?

Reply With Quote

#29

Old

paul c

Posts: n/a

Re: ?? Functional Dependency Question ?? - 10-18-2008 , 10:56 AM

Bob Badour wrote:
....

Quote:

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?

The table looks right to me.

Reply With Quote

#30

Old

paul c

Posts: n/a

Re: ?? Functional Dependency Question ?? - 10-18-2008 , 10:56 AM

Bob Badour wrote:
....

Quote:

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?

The table looks right to me.

Reply With Quote

Reply

Page 3 of 35

3

« Previous Thread | Next Thread »

Thread Tools
Show Printable Version Email this Page
Display Modes
Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

Posting Rules
You may not post new threads You may not post replies You may not post attachments You may not edit your posts vB code is On Smilies are On [IMG] code is On HTML code is Off

Powered by vBulletin Version 3.5.3
Copyright ©2000 - 2012, Jelsoft Enterprises Ltd.