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Unformatted text preview: Chapter 6 Deductive Reasoning: Propositional Logic ANSWERS TO EXERCISES Exercise 6.1 1. Conjunction. Components: The Democrats raised taxes, The Republicans cut programs. &amp; 2. Disjunction. Components: I walk home, I drive Ralphs car. v 3. Conditional. Components: Yankees win, they will be in the World Series. 4. Negation. Component: Yankees won. ~ 5. Conditional. Components: Taslima can read your mind, youre in trouble. 6. Disjunction. Components: The newspaper ad was misleading, it was meant as a joke. v 7. Conditional. Components: God is allpowerful, He can prevent evil in the world. 8. Conjunction. Components: He supported the revolution, he was arrested without being charged. &amp; Exercise 6.2 1. p v q 2. s t 3. ~ a 4. e &amp; f 5. ~ c 6. x y 7. ~ q p 8. ~ g &amp; ~ h 9. j &amp; k 10. ~ b 11. y x 12. p v q 13. d e 14. ~ ~ p 15. s v t 16. p &amp; q Exercise 6.3 1. True 2. False 3. True 4. False 5. True 6. True 7. True 8. False 9. True 10. True Exercise 6.4 1. False 2. True 3. False 4. True 5. True 6. True 7. True 8. True 9. False 10. True Exercise 6.5 1. Alligators are reptiles, and puppies are mammals. 2. Either John is home or Mary is home. 3. If the cat was on the mat, then Quentin was home. 4. Either babies cant fly, or cats can fly. 5. If the sun is not shining, then we will not go outside. 6. Alice is here, and Quentin is not here. 7. Either the bakery is open, or the pub is not open. 8. Alice sang, and Carl played the piano. 9. If Bob drove home, then Cathy will not leave. 10. If the day goes well, then we will not regret our efforts. Exercise 6.6 1. p q 2. p v q 3. p v q 4. ~ p &amp; ~ q 5. ~ a ~ b 6. p q 7. p &amp; ~ q 8. ~ p &amp; ~ q 9. p q 10. p &amp; ~ q Exercise 6.7 1. p v q p q p v q  T T T T F T F T T F F F 2. Alligators are reptiles and dogs are reptiles. a d a &amp; d  T T T T F F F T F F F F 3. ~ p &amp; ~ q p q ~ p ~ q ~ p &amp; ~ q   T T F F F T F F T F F T T F F F F T T T 4. p q p q p q  T T T T F F F T T F F T 5. p q p q p q  T T T T F F F T T F F T 6. Either dogs are not mammals, or snakes are reptiles. [Hint: To avoid confusion, you can add columns after the guide columns, such as the one for ~ d in this truth table. This extra column reminds you that the truth values for ~ d are the flip side of those for d.] d s ~ d ~ d v s  T T F T T F F F F T T T F F T T 7. ~ p q p q ~ p ~ p q  T T F T T F F T F T T T F F T F 8. Alligators can bark, and dogs are not reptiles....
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This note was uploaded on 12/20/2011 for the course PHIL 102 taught by Professor Rug during the Fall '11 term at University of Illinois, Urbana Champaign.
 Fall '11
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