# Re: A different definition of MINUS, Part 3

Date: Sun, 21 Dec 2008 11:36:54 -0800 (PST)

Message-ID: <9a38e1e3-08d2-4610-9632-92e483f6dc61_at_a26g2000prf.googlegroups.com>

On Dec 21, 6:25 am, "Walter Mitty" <wami..._at_verizon.net> wrote:

> Are the three fundamental ones <AND> <OR> & <NOT>?

*> If so, is it possible to define a <NAND> such that <AND> <OR> & <NOT> can
**> be derived from <NAND>?
**>
**> as in <NOT> A = A <NAND> A
**>
**> etc.?
*

I was going to say: "Impossible, because you don't have *all* boolean algebra axioms to substantiate such a derivation". But then I went into QBQL to check which of the following

x ^ y = ((x ^ y)' ^ (x ^ y)')'.

x + y = ((x ^ x)' ^ (y ^ y)')'.

x' = (x ^ x)'.

is invalid, and it failed to exhibit any counterexample! The last one is obvious since <AND> is idempotent, and the first one is provable in Prover9. The second one is tough... Received on Sun Dec 21 2008 - 20:36:54 CET