Math 340 Spring 2022 copyright Juh asz and Sobieska Homework 1 Logic Due on Fri Feb 10 11 59pm Problem 1 Let p and q be the propositions p The castle grounds are safe q A dragon has been spotted flying overhead Express each of these propositions as an English sentence a p q b p q c p q d p q The castle grounds are safe and a dragon has been spotted flying The castle grounds are not safe or a dragon has been spotted flying If the castle grounds are safe then a dragon has not been spotted flying The castle grounds are safe is necessary and sufficient for a dragon has not been spotted flying Problem 2 Show that each of these condition statements is a tautology by using truth tables a p q p b p q p A compound proposition is a tautology if the proposition is always true regardless of the truth value of the individual propositions that occur in it So both of these condition statements are tautology Problem 3 Let F x y be the statement x can fool y where the domain consists of all people in the world Use quantifies to express each of these statements x F x Justin a Everybody can fool Justin b There is no one who can fool everybody c Nobody can fool both Tom and Jerry d No one can fool themself x F x x x y F x y x F x Jerry F x Tom 1
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