5recitation

# 5recitation - Introduction to Computers and Programming...

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2 1 Introduction to Computers and Programming Prof. I. K. Lundqvist Recitation 5 May 13 2004 Logic in proofs Rule of Inference Tautology 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

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3 Rules of Inference p p q p q p p p q p q p 4 Rules of Inference p q will loose p q p q p q •Add i t ion – RedSox will win – RedSox or the Mets will win • Simplification – RedSox will win and The Yankees will not – RedSox will win • Conjunction
5 Rules of Inference (R v S) Æ W (R v S) W p Æ q p q 6 Rules of Inference (R v S) Æ W ¬ W ¬ (R v S) p Æ q ¬ q ∴¬ p • Modus Ponens – If it is raining or snowing, the ground is wet – It is raining or snowing – The ground is wet •Modus To l lens

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7 Rules of Inference p Æ q q Æ r p Æ q q Æ r p Æ r 8 Rules of Inference p q ¬ p q p q ¬ p q • Hypothetical syllogism
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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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5recitation - Introduction to Computers and Programming...

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