Re: "Armstrong's axioms" augmentation - help plz

paul c wrote:

> Dawn M. Wolthuis wrote:

>>> Jan Hidders wrote:
>>>> love boat via DBMonster.com wrote:
>>>>
>>>>> I understand the Augmentation rule:
>>>>> { X -> Y } |= XZ -> YZ
>>>>>
>>>>> but I don't understand why the rule can also be stated as:
>>>>>
>>>>> { X -> Y } |= XZ -> Y
>>>>>
>>>>> Why is this?
>>>>
>>>> It cannot. If you replace the first rule with the second you will 
>>>> not derive all FDs that hold.
>>>
>>> The first 'rule' is X -> Y, and so is the second!  What's the 
>>> difference?
>>

>>
> are you really saying that before the answer can get smaller, it has to 
> get larger? (LOL)

Actually what Dawn was telling you is that if you want to get a bigger answer you need a rule that makes the answer bigger. Makes sense, no? The first rule allows you to do that, the second doesn't. Knowing that it's pretty simple to come up with a formal proof that you can derive less dependencies if you replace the first rule with the second one.

• Jan Hidders