The use of DeMorgan's rule, which was in fact known to Ockham, of course perrmits
a & b =df ¬(¬a | ¬b) or a | b =df ¬(¬a & ¬b) In this practical sense both ¬,| and ¬,& are universal. At a more formal level the need to establish DeMorgan's rule (or a more general duality principle) as a theorem before it is used to dispense with either & or | makes it "necessary" to specify all three of &,|,¬ as universal. Minimalist constructions thus usually opt to use one or the other of NOR or NAND to construct the other 15 operations. There was indeed a period, now past, when NOR logic was used to construct many commercial computers. John Gilmore, Ashland, Ma 01721 - USA On 8/2/12, Shmuel Metz (Seymour J.) <shmuel+...@patriot.net> wrote: > In > <CAE1XxDEQXYTNtQJP056EzVzvyT=9yyhhezfxtluqvk_tbfa...@mail.gmail.com>, > on 08/02/2012 > at 08:07 AM, John Gilmore <jwgli...@gmail.com> said: > >>Any standard logic text establishes that > >>o AND, inclusive OR, and NOT are together universal, > > If it's any good it will note that NOT plus one of (AND,OR) is > universal; you don't need all three. Of course, if you're building > actual hardware then it's more economical to have a good library of > building blocks, rather than the minimum required. > > -- > Shmuel (Seymour J.) Metz, SysProg and JOAT > Atid/2 <http://patriot.net/~shmuel> > We don't care. We don't have to care, we're Congress. > (S877: The Shut up and Eat Your spam act of 2003) > > ---------------------------------------------------------------------- > For IBM-MAIN subscribe / signoff / archive access instructions, > send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN > ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN
