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

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.)
Define a formula. 1. p, q, r, … are formulas. 2. If X and Y are formulas, then so are ~X, (X 3. That’s it folks . (this is logicians’ expres- sion) Besides 1 ± 2, there is no other way of making up a formula.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Three kinds of formulas Formulas that are not contradictions are 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
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). K ((pvq) (p=>r) (q=>r))=>r, proof by

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Finding a formula given its truth table 1. Find all the rows in which the unknown
This is the end of the preview. Sign up to access the rest of the document.

### Page1 / 18

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online