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Chapter 17 : Logic

Chapter 17 : Logic.

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Chapter 17 : Logic

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  1. Chapter 17: Logic Riddle: Travelling to a city, an old man lost his way. He came to a fork in the road and did not know which road to take. Standing at the fork were two men. Next to the men was a sign, which you may assume is correct, which stated that one of the two men always told the truth and one of the men always told lies (but it was not known which was which). The sign went on to say that travellers could only ask one of the men one question. What question could the old man pose that would give him the information he needs to choose the correct route? A. Serra

  2. A. Propositions Class work: Propositions are statements which might be true or false. Discuss truth value (True/False): I had a great holiday and/or won the lottery and/or went to Zurich and/or… Notation: p, q, -q Example 17.2:2 page 533 Individual work: • Examples 1,2,3: Do them & check your answers. • Exercise 17A1: 1abc,3abc • Exercise 17A2: 1, 3 • Extra: 17A: even numbers

  3. B. Compound Propositions. CLASS WORK Compound propositions: conjunctions (and, ∧), disjunctions (or, ∨) and exclusive disjunctions. Examples with opening problem. Exercise 17B.2. 14 page 538 INDIVIDUAL WORK • Examples 1,2 and 3: Do them & check your answers. • Exercises 17B.1:1,3 ; 17B.2:5, 11 • Extra: Other exercises in 17B

  4. C. Truth tables and logical equivalence. CLASS WORK Discuss truth table page 539 Tautologies (all T) , logical contradictions (all F), logical equivalence (same T/F id) Example 17C2: 6 page 542. INDIVIDUAL WORK • Examples 5, 6, 7, 8 : Do them & check your answers. • Exercise 17C1: 1, 3. • Exercise 17C2: 1, 3. • Extra: Other exercises in 17C

  5. D. Implication and Equivalence. CLASS WORK Video: "She is a Witch" (by Monty Python) Implication ( p, antecedent q, consequent). Equivalence (if and only if). Exercise 17D 4 page 545. Example in page 570 and ideas for project. INDIVIDUAL WORK • Examples 9 and 19: Do them & check your answers. • Exercise 17D: 1,7 • Extra: Exercise 17D: 3,4

  6. E. Converse, Inverse and Contrapositive. CLASS WORK Which are equivalent? Imlication ( pq), converse: qp, inverse –p–q, contrapositive –q–p Exercise 17E4. Page 547. INDIVIDUAL WORK • Example 10: Do it & check your answers. • Exercises 17E: 1,3,5 • Extra: 17E any other exercise.

  7. Extra: 17F and SyllogismsReview • INDIVIDUAL WORK • Review Set 17A. Extra: Review Set 17B and/or 17C • NEXT • Mock test • Test • Good luck 

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