Logik, Statement Logic |
16.11.2011, 14:27 | Van11 | Auf diesen Beitrag antworten » |
Logik, Statement Logic Consider the following theorem that states the principle of structural induction for propositional formulas. Theorem. Principle of structural induction Let A be a property such that the following holds: 1. Every propositional variable has property A; 2. For every ?,? element von PROP, the set of well-formed propositional formu- las: if ? and ? have property A, so does ( ?° ? ), where ° element von {^,V,?,<?} 3. For every ? element von PROP: if ? has property A, so does not ?. Then any ? PROP has property A. Proof: Consider the set X:= {? element von PROP / has property A} Clearly, X ?PROP. Every propositional variable p element von X. Also, for any ?,? element von X and ~? element von X. So, set X meets conditions of the denition of propositional formula. Since PROP is the smallest set meeting these conditions, it follows that PROP ? X. Hence PROP =X. This concludes the proof. Using the principle of structural induction, prove that: 1. every well-formed propositional formula has an even number of parenthe- ses. 2. every well-formed propositional formula has more propositional variables than binary connectives. Meine Ideen: Versteh die Aufgabe leider nicht wirklich... |
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16.11.2011, 17:25 | Math1986 | Auf diesen Beitrag antworten » |
RE: Logik, Statement Logic Bitte beachte Wie kann man Formeln schreiben? , deine Frage ist ja unleserlich. |
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17.11.2011, 12:30 | Van11 | Auf diesen Beitrag antworten » |
RE: Logik, Statement Logic sry iwie scheint das nicht so recht zu klappen.... im anhang die nummer 2,so solls richtig aussehen! |
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