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Chapter 6 Test a Except for the Truth Table Questions Test 6A Logic Name:______________________________ Chapter 6 Test A Except for the truth table questions (which are double credit), each question is worth 2 points. Write your answer on the form provided. Erasure marks may cause the grading machine to mark your answer wrong. Select the correct translation for the following problems. 1. Either Breitling has a diamond model and Rado advertises a calendar watch or Tissot has luminous hands. a. B ∨ (R • T) b. (B ∨ R) • T c. (B • R) ∨ T d. B • R ∨ T e. B • (R ∨ T) 2. If Movado offers a blue dial, then neither Fossil is water resistant nor Nautica promotes a titanium case. a. M ⊃ (∼F ∨ ∼N) b. M ≡ ∼(F ∨ N) c. M ⊃ (∼F • ∼N) d. M ⊃ ∼(F ∨ N) e. M ⊃ ∼F • ∼N 3. Piaget has a gold watch only if both Seiko has leather bands and Breitling has a diamond model. a. P ⊃ (S • B) b. (S • B) ∨ P c. (S • B) ⊃ P d. (S • B) ≡ P e. S • (B ⊃ P) 4. Gucci features stainless steel; also, Fossil is water resistant given that Cartier offers a stop watch. a. G ∨ (C ⊃ F) b. (G • C) ⊃ F c. G • (F ⊃ C) d. C ⊃ (G • F) e. G • (C ⊃ F) 1 Test 6A 5. Movado and Nautica offer a black dial if and only if Piaget has a gold watch. a. (M ∨ N) ≡ P b. (M • N) ≡ P c. (M • N) ⊃ P d. P ⊃ (N • N) e. (P ⊃ M) • (P ⊃ N) 6. If Tissot has luminous hands, then if either Rado advertises a calendar model or Fossil is water resistant, then Gucci features stainless steel. a. (R ∨ F) ⊃ (T ⊃ G) b. (R ⊃ T) ⊃ (F ⊃ G) c. [T ⊃ (R ∨ F)] ⊃ G d. T ⊃ [(R ⊃ G) ∨ (F ⊃ G)] e. T ⊃ [(R ∨ F) ⊃ G] 7. Cartier’s offering a stop watch implies that Seiko has leather bands, provided that both Rado advertises a calendar model and Tissot has luminous hands. a. (R • T) ⊃ (C ⊃ S) b. (R ⊃ C) • (T ⊃ S) c. (C ⊃ S) ⊃ (R • T) d. [R ⊃ (C ⊃ S)] • [T ⊃ (C ⊃ S)] e. (R ∨ T) ⊃ (C ⊃ S) 8. Movado’s offering an ivory dial is a sufficient condition for Breitling’s having a ruby model if Gucci’s offering a better warranty is a necessary condition for Fossil’s being water resistant. a. (M ⊃ B) ⊃ (F ⊃ G) b. (B ⊃ M) ⊃ (G ⊃ F) c. (G ⊃ F) ⊃ (B ⊃ M) d. (F ⊃ G) ⊃ (M ⊃ B) e. F ⊃ [G ⊃ (M ⊃ B)] 9. Piaget and Nautica do not have a sapphire watch unless Breitling’s having a diamond watch is a sufficient and necessary condition for either Cartier’s offering multiple dials or Gucci’s selling a self-winder. a. ∼(P • N) ∨ [(C ∨ G) ≡ B] b. (∼P • ∼N) ∨ [(B ⊃ C) • (G ⊃ B)] c. (∼P • ∼N) ∨ [(B ≡ (C ∨ G)] d. (∼P • ∼N) ⊃ [(B ≡ (C ∨ G)] e. [(B ≡ (C ∨ G)] ⊃ (∼P • ∼N) 2 Test 6A 10. Seiko has a quartz watch if and only if either Movado does not offer a silver dial or Rado does not have a calendar watch; however, Tissot has luminous hands only if both Fossil is water resistant and Rado has a calendar model. a. [S ≡ ∼(M ∨ R)] • [T ⊃ (F • R)] b. [S ≡ (∼M ∨ ∼R)] • [(F • R) ⊃ T] c. [(∼M ∨ ∼R) ⊃ S] • [T ⊃ (F • R)] d. [S ≡ (∼M ∨ ∼R)] ∨ [T ⊃ (F • R)] e. [S ≡ (∼M ∨ ∼R)] • [T ⊃ (F • R)] Given that A and B are true and X and Y are false, determine the truth values of the propositions in problems 11 and 13. 11. [A ⊃ ∼ (B • Y)] ≡ ∼[B ⊃ (X • ∼ A)] a. True. b. False. 12. In problem 11, the main operator is a: a. Tilde. b. Wedge. c. Triple bar. d. Dot. e. Horseshoe. 13. [(X ⊃ A) • (B ⊃ ∼ Y)] ⊃ [(B ∨ Y) • (A ⊃ X)] a. True. b. False. 14. In problem 13, the main operator is a: a. Wedge. b. Tilde. c. Dot. d. Horseshoe. e. Triple bar. Use ordinary truth tables to answer problems 15-32. The truth table problems are double credit. Construct the truth tables as per the instructions in the textbook. 15. Given the statement: (N ⊃ K) ≡ (K ⊃ N) This statement is: a. Contingent. b. Inconsistent. c. Consistent. d. Tautologous. e. Self-contradictory. 3 Test 6A 16. Select the same answer as problem 15. 17. The truth table in problem 15 has how many lines? a. Six. b. Four. c. Two. d. Eight. e. Nine. 18. Given the statement: (G ⊃ ∼ Q) ≡ ∼(Q • G) This statement is: a. Consistent. b. Self-contradictory. c. Tautologous. d. Contingent. e. Logically equivalent. 19. Select the same answer as problem 18. 20. Given the statement: [∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)] This statement is: a. Tautologous. b. Valid. c. Contingent. d. Inconsistent. e. Self-contradictory. 21. Select the same answer as problem 20. 22. The truth table in problem 20 has how many lines? a. Four. b. Eight. c. Twelve. d. Six. e. Nine. 23. Given the pair of statements: ∼ (R ≡ M) and M • ∼ R These statements are: a. Inconsistent. b. Invalid. c. Logically equivalent. d. Consistent. e. Contradictory. 24. Select the same answer as problem 23. 4 Test 6A 25. Given the pair of statements: ∼ (S ⊃ Q) and ∼ Q • S These statements are: a. Logically equivalent. b. Valid. c. Contradictory. d. Consistent. e. Inconsistent. 26. Select the same answer as problem 25. 27. Given the pair of statements: C • ∼ L and L • ∼ C These statements are: a. Consistent. b. Inconsistent. c. Contradictory. d. Logically equivalent. e. Valid. 28. Select the same answer as problem 27. 29. Given the argument: B ∨ M / B ∨ ∼ K // (K ∨ ∼ M) ⊃ B This argument is: a. Invalid; fails in 3rd line. b. Invalid; fails in 2nd line. c. Invalid; fails in 1st line. d. Invalid; fails in 4th line. e. Valid. 30. Select the same answer as problem 29. 31. Given the argument: S ≡ (N ∨ H) / S ∨ ∼N // S ⊃ H This argument is: a. Invalid; fails in 4th line. b. Invalid; fails in 2nd line. c. Invalid; fails in 5th line. d. Valid. e. Invalid; fails in 3rd line. 32. Select the same answer as problem 31. 5 Test 6A Use indirect truth tables to answer problems 33-40. 33. Given the argument: E ⊃ J / B ⊃ Q / D ⊃ (J • ∼ Q) // (E • B) ≡ D This argument is: a. Uncogent. b. Sound. c. Valid. d. Invalid. e. Cogent. 34. Select the same answer as problem 33. 35. Given the argument: (K • ∼ C) ⊃ ∼(P • R) / J ⊃ (K • P) / A ⊃ (P • R) // (A • J) ⊃ C This argument is: a. Cogent. b. Sound. c. Valid. d. Uncogent. e. Invalid. 36. Select the same answer as problem 35. 37. Given the statements: S ⊃ (Q ∨ L) / (Q ∨ G) ⊃ (S ⊃ N) / L ⊃ (N ∨ ∼ S) / S • ∼ N These statements are: a. Inconsistent. b. Invalid. c. Tautologous. d. Logically equivalent. e. Consistent. 38. Select the same answer as problem 37. 39. Given the statements: R ⊃ (M ∨ ∼ C) / (P ∨ U) ⊃ C / M ⊃ ∼ P / R ≡ U These statements are: a. Contradictory. b. Tautologous. c. Valid. d. Inconsistent. e. Consistent. 40. Select the same answer as problem 39. Determine whether the following symbolized arguments are valid or invalid by identifying the form of each. In some cases the argument must be rewritten using double negation or commutativity before it has a named form. Those arguments without a specific name are invalid. 6 Test 6A 41. H ⊃ ∼M M ∼H a. DA—invalid. b. MP—valid. c. AC—invalid. d. MT—valid. e. HS—valid. 42. (∼G ∨ E) • (R ∨ M) R ∨ ∼G E ∨ M a. MT—valid. b. Invalid. c. DA—invalid. d. MP—valid. e. AC—invalid. 43. (R ⊃ ∼T) • (D ⊃ T) ∼T ∨ T ∼R ∨ ∼D a. MT—valid. b. CD—invalid. c. CD—valid. d. HS—valid. e. DD—valid. 44. ∼D ⊃ N D ∼N a. MP—valid. b. MT—invalid. c. DA—invalid. d. AC—invalid. e. Invalid. 45. ∼S ∼S ⊃ F F a. MP—valid. b. AC—valid. c. MT—valid. d. AC—invalid. e. DS—valid. 7 Test 6A 46. S ∨ ∼T S ∼T a. DA—invalid. b. CD—valid. c. Invalid. d. DD—valid. e. CD—invalid. 47. ∼J ⊃ C C ⊃ ∼T ∼J ⊃ ∼T a. DD—valid. b. MP—valid. c. CD—valid. d. Invalid. e. HS—valid. 48. L ∼N ⊃ L ∼N a. AC—invalid. b. DA—invalid. c. MP—valid. d. MT—valid. e. DS—invalid. 49. G ∨ ∼T (G ⊃ ∼H) • (∼T ⊃ A) ∼H ∨ A a. MP—valid. b. CD—valid. c. DD—valid. d. Invalid. e. DD—invalid. 50. K ∨ ∼B B K a. DA—invalid. b. Invalid. c. MT—valid. d. DS—valid. e. MP—valid. 8 Test 6A Logic Name:______________________________ Chapter 6 Test B Except for the truth table questions (which are double credit), each question is worth 2 points. Write your answer on the form provided. Erasure marks may cause the grading machine to mark your answer wrong. Select the correct translation for the following problems. 1. Princess drops its dress codes or Oceania enlarges its fleet, and Seabourn reduces its fares. a. P • (O ∨ S) b. (P • O) ∨ S c. P ∨ (O • S) d. P ∨ O • S e. (P ∨ O) • S 2. Not either Regent enlarges its casinos or Celebrity revises its itineraries if Holland remodels its staterooms. a. H ⊃ ∼(R ∨ C) b. H ≡ (∼R ∨ C) c. ∼ (R ∨ C) ⊃ H d. (∼R ∨ ∼C) ⊃ H e. H ⊃ (∼R ∨ ∼C) 3. Norwegian improves its entertainment only if both Disney does not promote family cruises and Windstar does not diversify its activities. a. N ⊃ (∼D ∨ ∼W) b. N ⊃ (∼D • ∼W) c. (∼D • ∼W) ⊃ N d. N ⊃ ∼(D • W) e. ∼(D • W) ⊃ N 4. Either Azmara or Seabourn do not open new boutiques provided that Princess improves its cuisine.
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