# Re: A different definition of MINUS, Part 3

From: paul c <toledobythesea_at_oohay.ac>
Date: Tue, 23 Dec 2008 06:41:04 -0800

Walter Mitty wrote:
> "paul c" <toledobythesea_at_oohay.ac> wrote in message

```>> paul c wrote:
>> ...
>>>
>>> ...  Projection and <REMOVE> are always fundamental.  ...
>>>
>> Oops, should have said <REMOVE> (projection) and <RENAME> are always
>> fundamental.
```

>
> I am sorry to be so dense, but I need further explanation...
>
> I asked whether <AND> <OR> &<NOT> are the three fundamental ones you
> referred to.
>
> understand you right, the three fundamentals are:
>
> Either <NAND> or <NOR>, take you pick.
> <REMOVE> (projection)
> &
> <RENAME>
>
> Is this right?
>
>

Yes, I think that you have said it right. This quote is from page 8 of

(quote)
We do not actually need both <AND> and <OR> in order to achieve relational completeness, thanks to De Morgan's Laws. For example, A <AND> B is identically equal to <NOT>((<NOT> A) <OR> (<NOT> B)), so we could dispense with <AND> if we included both <NOT> and <OR>. We could even collapse <NOT> and <OR> into a single operator, <NOR> ("neither A nor B"; equivalently, "not A and not B"). Equally well, of course, we could dispense with <OR> and collapse <AND> and <NOT> into a single operator, <NAND> ("not A or not B"). Overall, therefore, we could if desired reduce our algebra to just three operators: <RENAME>, <REMOVE>, and either <NOR> or <NAND> (plus <TCLOSE>). (end quote)

(This quote is not part of the formal definition (pages 12 to 14), it is just part of D&D's surrounding explanation. I think that all one really needs to understand are pages 12 to 14, which seem self-contained to me.) Received on Tue Dec 23 2008 - 15:41:04 CET

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