Assignment 1 Solutions - Chapter 1.1: Exercise 6: Let p and...

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Chapter 1.1: Exercise 6: Let p and q be the propositions “The election is decided” and “The votes have been counted”, respectively. Express each of these compound propositions as an English sentence. Exercise 8: p: you have the flu q: you miss the final exam r: you pass the course No Proposition English Sentence a ¬ p The election is not decided b p q The election is decided or the votes have been counted. c ¬ p q The election is not decided and the votes have been counted. d q p If the votes have been counted, then the election is decided. e ¬ q ¬ p If the votes have not been counted, then the election is not decided. f ¬ p ¬ q If the election is not decided, then the votes have not been counted g p q The election is decided if only if the votes have been counted See p.9 for various ways expressing iff. h ¬ q ( ¬ p q) Either the votes have not been counted, or else the election is not decided and the votes have been counted. No Proposition English Sentence a p q If you have the flu, then you miss the final exam. b ¬ q r You do not miss the final exam if and only if you pass the course. c q ¬ r If you miss the final exam, then you do not pass the course. d p q r You have the flu, miss the final exam, or pass the course. e (p ¬ r) ( q ¬ r) It is either the case that if you have the flu then you do not pass the course or the case that if you miss the final exam then you do not pass the course (or both, it is understood). Alternative way is to express as (p
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Assignment 1 Solutions - Chapter 1.1: Exercise 6: Let p and...

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