Test 6A 1 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)Test 6A 2 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)Test 6A 3 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.Test 6A 4 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.Test 6A 5 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 //