problems02-sol - MATH S-104 Lecture 2 In-class Problem...

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Unformatted text preview: MATH S-104 Lecture 2 In-class Problem Solutions June 25, 2009 Problem 1 † : Consider the following sentence: “Every residence hall at Harvard has the property that if a student has dated at least one person from that hall, then that student has dated at least two people from that hall.” Define appropriate predicates and write the sentence in first-order logic. H ( h ) : h is a residence hall S ( x ) : x is a student R ( x,h ) : x is a resident of residence hall h D ( x,y ) : x has dated y ∀ h, ( H ( h ) → ( ∀ x, ( S ( x ) → ( ∃ y, ( S ( y ) ∧ D ( x,y ) ∧ R ( y,h )) → ( ∃ y,z,y ≠ z, ( S ( y ) ∧ D ( x,y ) ∧ R ( y,h ) ∧ S ( z ) ∧ D ( x,z ) ∧ R ( z,h ))))))) Problem 2 * : Assume the following: 1. “Logic is difficult or not many students like logic.” 2. “If mathematics is easy, then logic is not difficult.” By translating these assumptions into statements involving propositional variables and log- ical connectives, determine whether each of the following are valid conclusions of these...
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problems02-sol - MATH S-104 Lecture 2 In-class Problem...

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