Homework #2 - Homework #2

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Homework #2 33 points Last Updated: 09/07/2009 Section 1.5 What rule of inference is used in each of these arguments? 4 (5) simplification a. disjunctive syllogism b. modus ponens c. addition d. hypothetical syllogism e. 6 (4) Homework #2 http://homepages.ius.edu/rwisman/C251/html/homework/hw2Solutions.htm 1 of 5 10/13/2009 3:10 AM
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Propositions r is "it rained" f is "it is foggy" l is "the life saving demonstration will go on" s is "the sailing race will be held" t is "the trophy will be awarded" Hypothesis (¬r v ¬f) ® (s ^ l) s ® t ¬t ¬t s ® t ____ ¬s modus tollens (¬r v ¬f) ® (s ^ l) º ¬(¬r v ¬f) v (s ^ l) Table 7, rule 1 ¬(¬r v ¬f) v (s ^ l) º (r ^ f) v (s ^ l) De Morgan (r ^ f) v (s ^ l) º ((r ^ f) v s) ^ ((r ^ f) v l) Distributive laws ((r ^ f) v s) ^ ((r ^ f) v l) _______ (r ^ f) v s) Simplification (r ^ f) v s) º (r v s) ^ (f v s) Distributive laws (r v s) ^ (f v s) _________ r v s Simplification r v s ¬s ____ r Disjunctive syllogism 14 a (4) Predicates c(x) is "x is in this class" r(x) is "x owns a red convertible" s(x) is "x has gotten a speeding ticket" Premises c(Linda) r(Linda) " x r(x) ® s(x) r(Linda) ® s(Linda) Universal instantiation r(Linda) ® s(Linda) r(Linda) ______ Modus ponens Homework #2 http://homepages.ius.edu/rwisman/C251/html/homework/hw2Solutions.htm 2 of 5 10/13/2009 3:10 AM
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Homework #2 - Homework #2

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