# Re: A different definition of MINUS, Part 3

From: paul c <toledobythesea_at_oohay.ac>
Date: Sun, 21 Dec 2008 14:49:25 -0800

```>> vadim..._at_gmail.com wrote:
>>> On Dec 21, 11:36 am, vadim..._at_gmail.com wrote:
>>>> x + y = ((x ^ x)' ^ (y ^ y)')'.
>>>> ... is tough...
>>> Actually, easy. The right side simplifies to
>>> x + y = (x' ^ y')'.
>>> Applying double negation (provable in RL), we get
>>> (x+y)' = x' ^ y'.
>>> De Morgan, which is again provable in RL. Amazing.
>> Why are you amazed?
```

>
> Two reasons:
> 1. Relational Algebra is a weaker system than boolean algebra.
> Therefore there is no reason to expect BA properties to carry over.
> 2. All RA operation, not just three can be reduced to a single one.
> Here is my worksheet:
>
> Join, is <AND>. It is representable in terms of Sheffer stroke.
> Projection, is inner union in RL terms. Well, I don't see how to
> represent inner union in terms of other operations:-(
>

I like the inner union very much, as a two-operand replacement for projection/Exists, provided <OR> is retained for convenience. While it may not have any present use in the A-algebra, there might be a future use but I need to do a lot of work to show that.

However, I think something like <RENAME> is still needed, for example to

define certain constraints such as functional dependencies. Received on Sun Dec 21 2008 - 23:49:25 CET

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