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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 doesnt start singing When the antecedent is true, and the consequent is false Suppose: Alice pays and John starts b true Alice doesnt pay but John starts nevertheless b still true! Alice doesnt pay, and John doesnt 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 doesnt start singing When the antecedent is true, and the consequent is false Suppose: Alice pays and John starts b true Alice doesnt pay but John starts nevertheless b still true! Alice doesnt pay, and John doesnt 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 doesnt start singing When the antecedent is true, and the consequent is false Suppose: Alice pays and John starts b true Alice doesnt pay but John starts nevertheless b still true! Alice doesnt pay, and John doesnt 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 dont pass. When the antecedent is true, and the consequent is false Suppose: You study and you pass b conditional is true You dont study and you pass b still true! You dont study and you dont 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 Youll fall if youre not careful. = If you are not careful, then youll fall....
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