From jjllambias@hotmail.com Thu Aug 09 16:22:35 2001 Return-Path: X-Sender: jjllambias@hotmail.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_3_1); 9 Aug 2001 23:22:35 -0000 Received: (qmail 74885 invoked from network); 9 Aug 2001 23:22:34 -0000 Received: from unknown (10.1.10.26) by l7.egroups.com with QMQP; 9 Aug 2001 23:22:34 -0000 Received: from unknown (HELO hotmail.com) (216.33.241.104) by mta1 with SMTP; 9 Aug 2001 23:22:34 -0000 Received: from mail pickup service by hotmail.com with Microsoft SMTPSVC; Thu, 9 Aug 2001 16:22:34 -0700 Received: from 200.69.11.208 by lw8fd.law8.hotmail.msn.com with HTTP; Thu, 09 Aug 2001 23:22:34 GMT X-Originating-IP: [200.69.11.208] To: lojban@yahoogroups.com Bcc: Subject: Re: [lojban] A or B, depending on C, and related issues Date: Thu, 09 Aug 2001 23:22:34 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 09 Aug 2001 23:22:34.0624 (UTC) FILETIME=[2B8F5000:01C1212A] From: "Jorge Llambias" la pycyn cusku di'e >Surely among the first to be dealt with would be the two >versions of "if P then Q, else R," which are also pleasantly simple: >(if P then Q) and (if not P then R)" and "(P iff Q) and (not P iff R)" >While >I am sure there are easier ways to show that these are the simplest forms >for >these functions, I confess to just having run all the possibilities from >disjunctive normal forms on down. Neither of them is "Q or R, depending on P" though. One of the versions of that would be: [(if P then Q) and (if not P then R)] xor [(if not P then Q) and (if P then R)] I have no idea whether that can be simplified. And that is assuming "depending on P" means "depending on whether or not P". If it can mean something like "depending on what the weather is like", it gets a little bit trickier... >I'm not quite sure what this has to do with anything, but it arose in some >other discussion -- perhaps in a more general form -- and perhaps this >answer, which is easily generalizable though with rapidly lengthening >results, will help. I suppose it depends on what you understand by "easily". :) mu'o mi'e xorxes _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp