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Unformatted text preview: Logic and Reasoning PHIL 102 [11] 5 Oct 2011 Today: rest of CHAPTER 6 Deductive Reasoning: Propositional Logic Four Logical Connectives : & Conjunction (and)— as in p & q (Alice rode her bike, and John walked.) v Disjunction (or)— as in p v q (Either Alice rode her bike, or John walked.) ~ Negation (not)— as in ~p (Alice did not ride her bike. Or: It is not the case that Alice rode her bike.) b Conditional (ifthen)— as in p b q (If Alice rode her bike, then John walked.) Chapter 6: Deductive Reasoning: Propositional Logic Truth table for a conjunction : p q p & q T T T T F F F T F F F F Truth table for a disjunction : p q p v q T T T T F T F T T F F F Truth table for a negation: p ~ p ~(~p) T F T F T Four Logical Connectives : Conditional (ifthen) p b q (If Alice pays for her ticket, then John will start singing.) When is this false ? I see Alice pays, but John doesn’t start singing… When the antecedent is true, and the consequent is false Suppose: Alice pays and John starts b true Alice doesn’t pay but John starts nevertheless b still true! Alice doesn’t pay, and John doesn’t start b still true! Chapter 6: Deductive Reasoning: Propositional Logic Four Logical Connectives : Conditional (ifthen) p b q ( If Alice pays for her ticket , then John will start singing .) When is this false ? I see Alice pays, but John doesn’t start singing… When the antecedent is true, and the consequent is false Suppose: Alice pays and John starts b true Alice doesn’t pay but John starts nevertheless b still true! Alice doesn’t pay, and John doesn’t start b still true! Chapter 6: Deductive Reasoning: Propositional Logic Four Logical Connectives : Conditional (ifthen) p b q ( If Alice pays for her ticket , then John will start singing .) When is this false ? I see Alice pays, but John doesn’t start singing… When the antecedent is true, and the consequent is false Suppose: Alice pays and John starts b true Alice doesn’t pay but John starts nevertheless b still true! Alice doesn’t pay, and John doesn’t start b still true! Chapter 6: Deductive Reasoning: Propositional Logic Four Logical Connectives : Conditional (ifthen) p b q ( If you study , then you will pass .) When is this false ? You study, but you don’t pass. When the antecedent is true, and the consequent is false Suppose: You study and you pass b conditional is true You don’t study and you pass b still true! You don’t study and you don’t pass b still true! Chapter 6: Deductive Reasoning: Propositional Logic Truth table for a conditional: p q p b q T T T T F F F T T F F T ‘You’ll fall if you’re not careful.’ = If you are not careful, then you’ll fall....
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This note was uploaded on 12/20/2011 for the course PHIL 102 taught by Professor Rug during the Fall '11 term at University of Illinois, Urbana Champaign.
 Fall '11
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