Logic Chapter 6 Test A Name: 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
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
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
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 a. Inconsistent. b. Invalid. c. Logically equivalent. d. Consistent. e. Contradictory. 24. Select the same answer as problem 23. 4
25. Given the pair of statements: (S Q) and Q S 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 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 3 rd line. b. Invalid; fails in 2 nd line. c. Invalid; fails in 1 st line. d. Invalid; fails in 4 th 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 4 th line. b. Invalid; fails in 2 nd line. c. Invalid; fails in 5 th line. d. Valid. e. Invalid; fails in 3 rd line. 32. Select the same answer as problem 31. 5
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 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 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
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
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
Logic Chapter 6 Test B Name: 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. a. P ( A S) b. ( A S) P c. ( A S) P d. P (A S) e. (A S) P 9
5. Carnival advertises its parties if and only if Disney s promoting family cruises implies that Norwegian improves its entertainment. a. (C D) N b. (C D) (N C) c. C (D N) d. C (D N) e. C (N D) 6. If Disney promotes family cruises, then if either Holland remodels its staterooms or Regent enlarges its casinos, then Windstar diversifies its activities. a. [D (H R)] W b. D [(H R) W] c. [(H R) D] W d. D [(H R) W] e. D (H R) W 7. Princess and Azmara improve gym facilities only if neither Carnival controls rowdiness nor Seabourn reduces fares. a. (P A) ( C S) b. (P A) (C S) c. (C S) (P A) d. (P A) ( C S) e. ( C S) (P A) 8. Regent s enlarging its casinos is a necessary condition for Disney s offering games if and only if Windstar s diversifying its activities is a sufficient condition for Costa s enlarging its nightspots. a. (R D) (C W) b. (D W) (R C) c. (D R) (W C) d. (D R) (W C) e. (R D) (W C) 9. Azmara s opening new boutiques is a sufficient and necessary condition for both Norwegian s improving entertainment and Holland s remodeling its staterooms if Princess s dropping its dress codes implies that Celebrity revises its itineraries. a. (P C) [(A N) (A C)] b. (P C) [A (N H)] c. [A (N H)] (P C) d. [(A N) (A C)] (P C) e. (P C) [A (N H)] 10
10. Seabourn revises its menu given that Norwegian and Princess halt tipping, unless Oceania enlarges its fleet if and only if both Costa improves its gym facilities and Regent enlarges its casinos. a. [S (N P)] [O (C R)] b. [(N P) S] [O (C R)] c. [(N P) S] [O (C R)] d. [S (N P)] [O (C R)] e. [S (N P)] [O (C 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) X] [ Y (A X)] a. True. b. False. 12. In problem 11, the main operator is a: a. Dot. b. Triple bar. c. Wedge. d. Tilde. e. Horseshoe. 13. [(A Y) (B X)] [(B X) (Y A)] a. True. b. False. 14. In problem 13, the main operator is a: a. Horseshoe. b. Dot. c. Tilde. d. Wedge. 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: (R B) (B R) This statement is: a. Logically equivalent. b. Tautologous. c. Self-contradictory. d. Contingent. 11
e. Consistent. 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: [N (S J)] [S (N J)] This statement is: a. Inconsistent. b. Contingent. c. Consistent. d. Self-contradictory. e. Tautologous. 19. Select the same answer as problem 18. 20. The truth table in problem 18 has how many lines? a. Nine. b. Twelve. c. Four. d. Eight. e. Six. 21. Given the statement: (F S) (S F) This statement is: a. Contingent. b. Self-contradictory. c. Inconsistent. d. Valid. e. Tautologous. 22. Select the same answer as problem 21. 23. Given the pair of statements: G H and H G a. Invalid. b. Consistent. c. Logically equivalent. d. Contradictory. e. Inconsistent. 24. Select the same answer as problem 23. 12
25. Given the pair of statements: J M and (J M) (M J) a. Valid. b. Consistent. c. Contradictory. d. Logically equivalent. e. Inconsistent. 26. Select the same answer as problem 25. 27. Given the pair of statements: D R and R D a. Logically equivalent. b. Consistent. c. Contradictory. d. Valid. e. Inconsistent. 28. Select the same answer as problem 27. 29. Given the argument: K (M H) / M H / M K // K H This argument is: a. Invalid; fails in 1 st line. b. Invalid; fails in 2 nd line. c. Valid. d. Invalid; fails in 4 th line. e. Invalid; fails in 3 rd line. 30. Select the same answer as problem 29. 31. Given the argument: R I / S (R I) // S I This argument is: a. Valid. b. Invalid; fails in 4 th line. c. Invalid; fails in 2 nd line. d. Invalid; fails in 5 th line. e. Invalid; fails in 3 rd line. 32. Select the same answer as problem 31. 13
Use indirect truth tables to answer problems 33-40. 33. Given the argument: Q S / (N A) / S A / (P N) (G Q) // P G This argument is: a. Valid. b. Uncogent. c. Invalid. d. Cogent. e. Sound. 34. Select the same answer as problem 33. 35. Given the argument: J C / R I / I (U J) / (R U) (C J) // C This argument is: a. Sound. b. Uncogent. c. Invalid. d. Cogent. e. Valid. 36. Select the same answer as problem 35. 37. Given the statements: Q (N S) / N (L B) / (S E) (Q B) / Q B a. Inconsistent. b. Consistent. c. Invalid. d. Tautologous. e. Logically equivalent. 38. Select the same answer as problem 37. 39. Given the statements: P (A M) / (D K) (M H) / (A H) D / P D a. Contradictory. b. Tautologous. c. Valid. d. Inconsistent. e. Consistent. 40. Select the same answer as problem 39. 14
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. 41. D C R D R C a. MP valid. b. DS valid. c. Invalid. d. CD valid. e. HS valid. 42. ( C J) (P L) J L C P a. CD valid. b. Invalid. c. DD valid. d. MT valid. e. CD invalid. 43. M M G G a. AC invalid. b. MT valid. c. DS invalid. d. DA invalid. e. MP valid. 44. N A N A a. DS valid. b. HS valid. c. MT valid. d. DA invalid. e. MP valid. 45. D E E D a. AC invalid. b. DS invalid. c. Invalid. 15
d. MP valid. e. HS valid. 46. K N K N a. HS valid. b. MP valid. c. MT valid. d. DS valid. e. AC invalid. 47. Q H Q H a. MT invalid. b. MP valid. c. DA invalid. d. DS valid. e. AC invalid. 48. E A B E B A a. Invalid. b. DD invalid. c. HS valid. d. CD valid. e. DS valid. 49. ( H K) (H T) H H T K a. Invalid. b. CD valid. c. DD valid. d. DA invalid. e. MP valid. 16
50. S F F S a. MP valid. b. DS invalid. c. DA invalid. d. MT valid. e. DS valid. 17