Re: what boolean connectives together with -> make a complete system?

From: Owen (oorionus_at_yahoo.com)
Date: 12/21/04 

Date: Tue, 21 Dec 2004 15:07:02 -0500

  Where are the expected muraders of anything that novices say, such as me,
express.
  Ullrich, G. Frege, Fransen, ..where are you complaints?

  Surely , I didn't say something correct, in your view.

  "Owen" <oorionus@yahoo.com> wrote in message
news:_8OdnddRjY3CT1vcRVn-uw@rogers.com...
> I. (nor)
>
> 1.~p =df (p nor p)
> 2. p v q =df ~(p nor q)
> 3. _T =df p v ~p
> 4. F =df ~T
> 5. p & q =df ~(~p v ~q)
> 6. p nand q =df ~(p & q)
> 7. p -> q =df ~p v q
> 8. p -|-> q =df ~(p -> q)
> 9. p <-> q =df (p -> q)&(q -> p)
> 10. p xor q =df ~(p <-> q)
>
>
> II. (nand)
>
> 1. ~p =df (p nand p)
> 2. p & q =df ~(p nand q)
> 3. F =df p & ~p
> 4. T =df ~F
> 5. p v q =df ~(~p & ~q)
> 6. p nor q =df ~(p v q)
> 7. p -> q =df ~p v q
> 8. p -|-> q =df ~(p -> q)
> 9. p <-> q =df (p -> q)&(q -> p)
> 10. p xor q =df ~(p <-> q)
>
>
> III. (T, -|->)
>
> 1. ~p =df T -|-> p
> 2. F =df ~T
> 3. p -> q =df ~(p -|-> q)
> 4. p v q =df ~p -> q
> 5. p nor q =df ~(p v q)
> 6. p & q =df ~(~p v ~q)
> 7. p nand q =df ~(p & q)
> 8. p <-> q =df (p -> q)&(q -> p)
> 9. p xor q =df ~(p <-> q)
>
>
> IV. (F, ->)
>
> 1. ~p =df p -> F
> 2. T=df ~F
> 3. p -|-> q =df ~(p -> q)
> 4. p v q =df ~p -> q
> 5. p nor q =df ~(p v q)
> 6. p & q =df ~(~p v ~q)
> 7. p nand q =df ~(p & q)
> 8. p <-> q =df (p -> q)&(q -> p)
> 9. p xor q =df ~(p <-> q)
>
> V. (~, v)
>
> 1. T =df p v ~p
> 2. F =df ~T
> 3. p nor q =df ~(p v q)
> 4. p -> q =df ~p v q
> 5. p -|-> q =df ~(p -> q)
> 6. p & q =df ~(~p v ~q)
> 7. p nand q =df ~(p & q)
> 8. p <-> q =df (p -> q)&(q -> p)
> 9. p xor q =df ~(p <-> q)
>
> VI. (~, &)
>
> 1. F =df p & ~p
> 2. T =df ~F
> 3. p nand q =df ~(p & q)
> 4. p v q =df ~(~p & ~q)
> 5. p nor q =df ~(p v q)
> 6. p -> q =df ~p v q
> 7. p -|-> q =df ~(p -> q)
> 8. p <-> q =df (p -> q)&(q -> p)
> 9. p xor q =df ~(p <-> q)
>
> VII. (~, ->)
>
> 1. T =df p -> p
> 2. F =df ~T
> 3. p -|-> q =df ~(p -> q)
> 4. p v q =df ~p -> q
> 5. p nor q =df ~(p v q)
> 6. p & q =df ~(~p v ~q)
> 7. p nand q =df ~(p & q)
> 8. p <-> q =df (p -> q)&(q -> p)
> 9. p xor q =df ~(p <-> q)
>
>
>
>
>
> "|-|erc" <h@r.c> wrote in message
news:32n8q4F3onqg5U1@individual.net...
> > like NOT and OR is complete.
> >
> > NOR is complete
> >
> > -> and ?
> >
> > Herc
> >
> > --
> > "YOU CAN'T PROVE ME"
> > If you prove it's true then it has a proof, which makes it false
> > If you don't prove it, then its true
> > 10,000 people in sci.math ALL believe this is irrefutable that
> mathematics will always be incomplete.
> >
> >
>
>

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