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Logic0923 - Knights and knaves w again 1 2 3 Tautologies...

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OE ° “± ±±± ±± Knights and knaves again 1. Tautologies, contradictions 2. Application of the symbolic method 3. NGP revisited
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Errata in Ch.8 p. 56, 15 lines from bottom, Problem 8 .5 -> 1.5 p. 57, three lines below “NGP Revisited”: of -> if p. 59, 12 lines from bottom, Chapter 3 - > 2 p. 61, the last line, Problem 8 .2 -> 2.2 p. 64, 4 lines from bottom, the knight -> knave HW #3 is due 9/30 (Wed.)
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Define a formula. 1. p, q, r, … are formulas. 2. If X and Y are formulas, then so are ~X, (X Y), (XvY), (X=>Y), (X±Y). 3. That’s it folks . (this is logicians’ expres- sion) Besides 1 & 2, there is no other way of making up a formula.
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Three kinds of formulas Formulas that are not contradictions are called satisfiable (true-able). definitions e.g. abbrevi- ated Tautologies Always true (in every row) pv~ p t Contradic- tions Always false (in every row) p ∧∼ p f Contingent Neither t nor f pvq
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Some tautologies ((p=>q) (q=>r))=>(p=>r), hypothetical syllogism (p (p=>q))=>q, modus ponens ((p=>q) ~q)=>~p, modus tollens ((~p=>q) (~p=>~q))=>p, reductio ad absurdum To show p, assume ~p and show that ~p implies both q and ~q (contradiction).
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