19_evenmorelogic

19_evenmorelogic - Introduction to Computers and...

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Introduction to Computers and Programming Prof. I. K. Lundqvist Lecture 19 2 Terminology that is either true or false (but not both) Conjunction : p q, corresponds to and Disjunction : p q, corresponds to or Negation : ¬ p , ¬ corresponds to not May 4 2004 • A proposition is a declarative statement
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3 CQ 1 1. True , False 2. True , True 3. False , False 4. I don’t know P = Everyone loves ice cream ; Q = X loves ice cream P is a proposition, Q is a proposition 4 Implication Implication : p q, corresponds to implies “if it rains, then it is cloudy” p = it rains q = it is cloudy p q 1 1 0 1 1 0 0 0 Q P 0 1 0 1 1 0 1 0 P P 1 0 1 1 0 0 0 1 1 1 1 0 0 P V Q P Q P
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Name p p q p (p q) Addition p q (p q) p Simplification p p, q (p q) p q Conjunction p q p, p q q (p (p q)) q Modus Ponens ¬ q, p q ¬ p ( ¬ q (p q)) ¬ p Modus Tollens p q, q r p r ((p q) (q r)) (p r) Hypothetical Syllogism p q, ¬ p q ((p q) ¬ p) q Disjunctive Syllogism p q, ¬ p r q r (p q) ( ¬ p r) q r Resolution 5 6 By the rule of resolution , we know that “ It is raining today or it is windy today .” Ex : Consider these statements “ If I buy something, then I go to the store If I go to the store, then I drive my car statements are true, then by hypothetical syllogism we can conclude that “ If I buy something , then I drive my car .” Ex : Consider the statements “ It is raining today or it is snowing today It is not snowing today or it is windy today know both of these statements are true then what can we conclude?
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

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19_evenmorelogic - Introduction to Computers and...

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