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4 Sample Examination Questions and Answers I. CHAPTER ONE: INTRODUCTION 1. Consider the following argument: 1. All men are authors. 2. Mark Twain is a man. / Mark Twain is an author. a. Are all of the premises true? b. […]

30 X. CHAPTER TEN: RELATIONAL PREDICATE LOGIC A. Symbolizing 1. If something is heavy, then Art won’t lift it. (Hx = “x is heavy”; a = “Art”; Lxy = “x will lift y”.) 2. If something is heavy, then anyone […]

37 XI. CHAPTER ELEVEN: QUANTIFIER RULES THEORY 1. Explain, using a concrete example, why we should not 1. ( y)Lxy allow the following inference when using EI. What restriction then is required on the use of EI? 2. Lxx 1EI […]

39 XII. CHAPTER TWELVE: PREDICATE LOGIC TRUTH TREES Use the truth-tree method to determine the validity/invalidity of the following arguments. If invalid, use the constants in an open path to expand the premises and conclusion and assign truth-values to show […]

2. Explain why translating “sis visible to Jane” as a material conditional, such as “if s is near Jane (and the line of sight is unobstructed, etc.) then it will be seen by her,” seems to be inadequate. 3. Use […]

48 XIV. CHAPTER FOURTEEN: SYLLOGISTIC LOGIC A. General Theory 1. Assuming existential import, explain what the differences are between (a) contradictories; (b) contraries; and (c) subcontraries. 2. Prove that no valid syllogism in the second figure can have an affirmative […]

57 4. Whenever the Boston Red Sox have been in the World Series I have always bet on them, and I have always lost. They must win the World Series this year since they have never won it. This must […]

58 XVI. CHAPTER SIXTEEN: INDUCTIVE LOGIC A. General Theory 1. If q deductively follows from p, then it follows from p r no matter what r happens to be. But if q inductively follows from p, then does it follow […]

60 XVII. CHAPTER SEVENTEEN: AXIOM SYSTEMS A. True or False 1. There are complete and consistent axiom systems for both sentential and predicate logic. 2. There is a complete and consistent axiom system for arithmetic. 3. It is possible to […]

6 II. CHAPTER TWO: SYMBOLIZING IN SENTENTIAL LOGIC A. General Theory For 1-3, circle one of a-d: 1. A compound sentence is truth functional if and only if: a. the truth value of the compound sentence is determined by the […]

8 III. CHAPTER THREE: TRUTH TABLES A. General Theory 1. Determine the sentence forms of which the following are substitution instances: a. ~ (A B)C b. A (B~C) 2. If a sentence form contains five variables, how many lines or […]

(l) 1. A ~ A/ ~ A (2) 1. ~ A B 2. C A 3. ~ B/ ~ C (3) 1. A / (~ A C) (4) 1. (A B) C 2. ~ A ~ C / ~ B […]

2. a. Use IP to prove that the following argument is valid. A B A ~ B / ~ A b. To illustrate how indirect proofs are a kind of shortened conditional proof, cross out the last line in the […]

20 VI. CHAPTER SIX: SENTENTIAL LOGIC TRUTH TREES Use the truth-tree method to determine the validity/invalidity of the following argument forms: (1) 1. p~q 2. ~ (~ q~p) / p (2) 1. (p q)r 2. ~ q~r/p (3) 1. p […]

23 VII. CHAPTER SEVEN: PREDICATE LOGIC SYMBOLIZATION A. General theory: 1. Which of the following are sentences? a. (x)Fx ( y)Gxy d. ~ ( y) Fy (x)Gx b. (x)Fx Ga e. None of these c. (x)(Fx Ga) 2. Which of […]

26 VIII. CHAPTER EIGHT: PREDICATE LOGIC SEMANTICS A. General Theory 1. If there are no unicorns, what is the truth value of the sentence (x)(Ux Mx),where Ux =x is a unicorn, and Mx = x is mortal? 2. What about […]

28 IX. CHAPTER NINE: PREDICATE LOGIC PROOFS. Prove valid: (1) 1. ~ ( x)Ax (5) 1. ( x)[Ax (y)By] / (x)(Ax Bx) /(x)Ax (y)By (2) 1. ~ Aa (6) 1. (x)Ax (y)By / ~ (x) (Ax Bx) /(x) [Ax (y)By] […]

62 Answers to Odd-Numbered Exercise Items in the Text PART ONE: SENTENTIAL LOGIC EXERCISE 1-1: 1. Not an argument, just a description of the speaker’s attitude toward certain sports and sports in general. 13. If God were all good he […]

(5)With IP: 4. HAP/~H 5. AB1, 4 MP 6. B5Simp 7. M~A2,6 MP 8. A5Simp 9. ~ ~ A8DN 10. M7,9 DS 11. ~ H~B3,10 MP 12. ~ ~ H4DN 13. ~ B11,12 DS 14. B~B6,13 Conj 15. ~ H4-14 […]

(13) 4. 2 Add 8. 1,7 MP EXERCISE 4-4: (1) 3. (QR) Q (3) 2. B(A B) (5) 3. DA 4. ~ (R ~ W) 4. (B C) D 6. BC (7) 3. ~ E EXERCISE 4-5: (1) 3. LR1,2 […]

10 PART TWO: PREDICATE LOGIC EXERCISE 7-1: EXERCISE 7-2: 1. (1) x is bound. (2) a is an individual constant. F and Gare property constants. (3) No free variables; a is within the scope of the (x) quantifier. 3. (1) […]

126 (5) 1. (x) (Fx Gx)AP/ (x)Fx (x)Gx 9. (x)Fx (x)Gx AP/ (x) (Fx Gx) 10. (x)Fx 9Simp 11. Fx 10 UI 12. (x)Gx 9Simp 13. Gx 12 UI 14. Fx Gx 11,13 Conj 15. (x) (Fx Gx) 14 UG […]

139 (9) 1. ( x)(Ax ~Bx) p EXERCISE 13-1: (1) 3. Fx Gx 2EI 4. (x) [Fx (x=a)] 1 Simp 5. Fx (x=a) 4 UI 6. Fx 3Simp 7. x=a5,6 MP 8. Gx 3Simp 9. Ga 7,8 ID (3) 5. […]

152 PART THREE: OTHER SYSTEMS OF LOGIC EXERCISE 15 1: (One person’s opinions, provided with a great deal of hesitation. More important is how students answer these questions. ) 1. Begging the question: The question was whether her suspicions were […]