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# lect04 - INTRO LOGIC DAY 04 1 Schedule for Unit 1 Day 1...

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1 1 INTRO LOGIC DAY 04 2 Schedule for Unit 1 Intro Day 1 Chapter 4 Day 7 EXAM #1 Day 8 Chapter 4 Day 6 Chapter 4 Day 5 Chapter 3 Day 4 Chapter 2 Day 3 Chapter 1 Day 2 40% of Exam 1 60% of Exam 1 warm-up

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2 3 CHAPTER 3 VALIDITY IN SENTENTIAL LOGIC 4 Validity in General an argument is valid if and only if it is IM possible for the conclusion to be false while the premises are true an argument is IN valid if and only if it is possible for the conclusion to be false while the premises are true
3 5 What are Possibilities? in Sentential Logic, at least, a possibility is a case , which is a possible combination of truth-values assigned to the atomic sentences 6 case 4 case 3 case 2 case 1 S R Example 1 If an argument form has 2 atomic sentences, then there are 4 cases. F T F T T T F F

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4 7 Example 2 If an argument form has 3 atomic sentences, then there are 8 cases. F F T case 4 T T F case 5 F T F case 6 T F F case 7 F F T T R F F case 8 T T case 3 F T case 2 T T case 1 S Q 8 In General # atomics # cases 1 2 2 4 3 8 16 4 32 5 2 n n
5 9 Example 1 Modus Tollens / not R ; not S if R then S / R ; S R S / conclusion ; premise 2 premise 1 10 Truth-Table R S ; S F T F T S F 4 F 3 T 2 T 1 / R R case Is there a case in which the premises are all true but the conclusion is false? Is the argument form valid or invalid? T T F T T F T F T T F F VALID NO

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6 11 Example 2   of Modus Tollens / not S ; not R if R then S / S ; R R S / conclusion ;
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lect04 - INTRO LOGIC DAY 04 1 Schedule for Unit 1 Day 1...

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