A question on XOR
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From: Nam Nguyen on 7 Aug 2010 20:42 I have a question: Let A be an atomic formula of an L. As far as FOL proof is concerned, if (A \/ ~A) signifies a tautology and (A /\ ~A) a contradiction, what would (A xor ~A) signify? -- ----------------------------------------------------------- Normally, we do not so much look at things as overlook them. Zen Quotes by Alan Watt -----------------------------------------------------------
From: William Elliot on 7 Aug 2010 23:06 On Sat, 7 Aug 2010, Nam Nguyen wrote: > I have a question: Let A be an atomic formula of an L. > As far as FOL proof is concerned, if (A \/ ~A) signifies > a tautology and (A /\ ~A) a contradiction, what would > (A xor ~A) signify? > A xor ~A <-> A&~~A v ~A&~A
From: Nam Nguyen on 8 Aug 2010 02:57 William Elliot wrote: > On Sat, 7 Aug 2010, Nam Nguyen wrote: > >> I have a question: Let A be an atomic formula of an L. >> As far as FOL proof is concerned, if (A \/ ~A) signifies >> a tautology and (A /\ ~A) a contradiction, what would >> (A xor ~A) signify? >> > A xor ~A <-> A&~~A v ~A&~A So, then, what does e.g. (A or ~A) signify to you? -- ----------------------------------------------------------- Normally, we do not so much look at things as overlook them. Zen Quotes by Alan Watt -----------------------------------------------------------
From: PiperAlpha167 on 8 Aug 2010 03:38 On Aug 7, 5:42 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > I have a question: Let A be an atomic formula of an L. > As far as FOL proof is concerned, if (A \/ ~A) signifies > a tautology and (A /\ ~A) a contradiction, what would > (A xor ~A) signify? > > -- > ----------------------------------------------------------- > Normally, we do not so much look at things as overlook them. > Zen Quotes by Alan Watt > ----------------------------------------------------------- (A V ~A) & ~(A & ~A) You might take a look at: http://www.earlham.edu/~peters/courses/logsys/pnc-pem.htm
From: William Elliot on 8 Aug 2010 05:14
On Sun, 8 Aug 2010, Nam Nguyen wrote: > William Elliot wrote: >> On Sat, 7 Aug 2010, Nam Nguyen wrote: >> >>> I have a question: Let A be an atomic formula of an L. >>> As far as FOL proof is concerned, if (A \/ ~A) signifies >>> a tautology and (A /\ ~A) a contradiction, what would >>> (A xor ~A) signify? >>> >> A xor ~A <-> A&~~A v ~A&~A > > So, then, what does e.g. (A or ~A) signify to you? A v ~A <-> ~(~A & ~~A) ---- |