Difference between revisions of "TU Wien:Einführung in wissensbasierte Systeme VU (Egly)/Übungen WS12/Blatt 1 - Beispiel 4"

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(a) If <math>\phi</math> is a '''contradiction''', then <math>\phi</math> is a tautology and <math>\psi</math> is a '''contradiction'''.
 
(a) If <math>\phi</math> is a '''contradiction''', then <math>\phi</math> is a tautology and <math>\psi</math> is a '''contradiction'''.
  
(b) if <math>\phi \land \psi</math> is a '''tautology''', then <math>\phi</math> is a '''tautology''' or <math>\psi</math> is a '''tautology'''.
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(b) If <math>\phi \lor \psi</math> is a '''tautology''', then <math>\phi</math> is a '''tautology''' or <math>\psi</math> is a '''tautology'''.
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(c) If <math>\phi</math> and <math>\psi</math> have no propositional letter in common, then <math>\phi \lor \psi</math> is a '''tautology''' iff <math>\phi</math> is a '''tautology''' or <math>\psi</math> is a '''tautology'''.
  
(c)
 
  
  

Revision as of 20:50, 27 October 2012

Give a proof or a counter-example for the following statements:

(a) If \phi is a contradiction, then \phi is a tautology and \psi is a contradiction.

(b) If \phi \lor \psi is a tautology, then \phi is a tautology or \psi is a tautology.

(c) If \phi and \psi have no propositional letter in common, then \phi \lor \psi is a tautology iff \phi is a tautology or \psi is a tautology.


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