hw2_solutions

hw2_solutions - Problem Set 2 Solutions Problem 1 1. p q...

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Problem Set 2 Solutions Problem 1 1. p q [given] 2. p r [given] 3. q r [given] 4. ¬ p r [2, implication] 5. ¬ q r [3, implication] 6. ( ¬ p r ) ( ¬ q r )[ 4 , 5 , c o n j u n c t i o n ] 7. ( r ∨¬ p ) ( r q 6 , c o m m u t a t i v i t y ] 8. r ( ¬ p ∧¬ q 7 , d i s t r i b u t i v e p r o p e r t y ] 9. ( ¬ p q ) r 8 , c o m m u t a t i v i t y ] 10. ¬ ( p q ) r [9, De Morgan’s law] 11. ( p q ) r [10, implication] 12. r [1, 11, modus ponens] Problem 2 1. p r [given] 2. q s [given] 3. ¬ p r [1, implication] 4. ( ¬ p r ) s [3, addition] 5. ¬ p ( r s 4 , a s s o c i a t i v i t y ] 6. ¬ q s [2, implication] 7. ( ¬ q s ) r [6, addition] 8. ¬ q ( s r 7 , a s s o c i a t i v i t y ] 9. ¬ q ( r s 8 , c o m m u t a t i v i t y ] 10. ( ¬ p ( r s )) ( ¬ q ( r s )) [5, 9, conjunction] 11. ( ¬ p q ) ( r s ) [10, distributive property] 12. ¬ ( p q ) ( r s 1 1 , D e M o r g a n s l a w ] 13. ( p q ) ( r s ) [12, implication] Problem 3 The following assignments all work. p = T,q = T,r = T,s = F p = F,q = = = F p = = = F,s = T p = = F,r = = T 1
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Problem 4 (a) A =”th ishouseisnexttoalake” B =”thetreasureisinthek itchen” C = ”the tree in the front yard is an elm” D = ”the treasure is buried under the Fagpole” E =”thetreeinthebackyardisanoak” G =”thetreasureisinthegarage”
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hw2_solutions - Problem Set 2 Solutions Problem 1 1. p q...

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