Venn Diagrams sample questions

Question: For Sorites 1I, the first intermediate conclusion is:

Answer Choices: a. All S are Q. b. Some M are not G. c. No G are H. d. No S are H. e. Some M are not Q.

Answer: a. All S are Q.

Question: For Sorites 1I, the second intermediate conclusion is:

Answer Choices: a. No G are H. b. Some M are not Q. c. No S are H. d. All S are Q. e. Some H are not G.

Answer: c. No S are H.

Question: For Sorites 1I, the correct answer is:

Answer Choices: a. Unsound b. Invalid c. Sound d. Cogent e. Invalid

Answer: b. Invalid

Question: Given the following sorites: “No S are A. All N are A. All T are N. Some R are T. Some R are not S.” This sorites is:

Answer Choices: a. Invalid because only one premise is negative. b. Invalid because one of the middle terms is undistributed. c. Invalid because a term is distributed in the conclusion but not in the premise. d. Valid because no rules are broken. e. Valid because a negative premise requires a negative conclusion.

Answer: d. Valid because no rules are broken.

Question: Either Breitling has a diamond model and Rado advertises a calendar watch or Tissot has luminous hands.

Answer Choices: a. B ∨ (R • T) b. (B ∨ R) • T c. (B • R) ∨ T d. B • R ∨ T e. B • (R ∨ T)

Answer: c. (B • R) ∨ T

Question: If Movado offers a blue dial, then neither Fossil is water resistant nor Nautica promotes a titanium case.

Answer Choices: a. M ⊃ (~F ∨ ~N) b. M ≡ (~F ∨ N) c. M ⊃ (~F • ~N) d. M ⊃ (~F ∨ N) e. M ⊃ ~F • ~N

Answer: d. M ⊃ (~F ∨ N)

Question: Piaget has a gold watch only if both Seiko has leather bands and Breitling has a diamond model.

Answer Choices: a. P ⊃ (S • B) b. (S • B) ∨ P c. (S • B) ⊃ P d. (S • B) ≡ P e. S • (B ⊃ P)

Answer: a. P ⊃ (S • B)

Question: Gucci features stainless steel; also, Fossil is water resistant given that Cartier offers a stop watch.

Answer Choices: a. G ∨ (C ⊃ F) b. (G • C) ⊃ F c. G • (F ⊃ C) d. C ⊃ (G • F) e. G • (C ⊃ F)

Answer: e. G • (C ⊃ F)

Question: Movado and Nautica offer a black dial if and only if Piaget has a gold watch.

Answer Choices: a. (M ∨ N) ≡ P b. (M • N) ≡ P c. (M • N) ⊃ P d. P ⊃ (N • N) e. (P ⊃ M) • (P ⊃ N)

Answer: b. (M • N) ≡ P

Question: If Tissot has luminous hands, then if either Rado advertises a calendar model or Fossil is water resistant, then Gucci features stainless steel.

Answer Choices: a. (R ∨ F) ⊃ (T ⊃ G) b. T ⊃ (R ⊃ G) c. [T ⊃ (R ∨ F)] ⊃ G d. T ⊃ [R ⊃ G) ∨ (F ⊃ G)] e. T ⊃ [(R ∨ F) ⊃ G]

Answer: e. T ⊃ [(R ∨ F) ⊃ G]

Question: Cartier’s offering a stopwatch implies that Seiko has leather bands, provided that both Rado advertises a calendar model and Tissot has luminous hands.

Answer Choices: a. (R • T) ⊃ (C ⊃ S) b. R ⊃ (C • T ⊃ S) c. (C ⊃ S) ⊃ (R • T) d. (R • T) ⊃ (C ⊃ S)] e. (R ∨ T) ⊃ (C ⊃ S)

Answer: a. (R • T) ⊃ (C ⊃ S)

Question: 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.

Answer Choices: a. M ⊃ (B ⊃ F) b. (B ⊃ M) ⊃ F c. (G ⊃ F) ⊃ (B ⊃ M) d. (G ⊃ F) ⊃ (B • M) e. F ⊃ (G ⊃ M ⊃ B)

Answer: d. (G ⊃ F) ⊃ (B • M)

Question: 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.

Answer Choices: 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)

Answer: c. ~(P • N) ∨ [(B ≡ C ∨ G)]

Question: 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.

Answer Choices: a. [S ≡ (~M ∨ R)] ⊃ [T ⊃ (F • R)] b. [S ≡ (~M • ~R)] ⊃ [T ⊃ (F • R)] c. (M • N) ⊃ F d. [S ≡ (~M ∨ R)] ⊃ [T ⊃ (F • R)] e. [S ≡ (~M • ~R)] ⊃ [T ⊃ (F • R)]

Answer: e. [S ≡ (~M • ~R)] ⊃ [T ⊃ (F • R)]

Question: In Proposition 1A, the main operator is:

Answer Choices: a. Tilde b. Wedge c. Triple bar d. Dot e. Horseshoe

Answer: c. Triple bar

Question: In Proposition 2A, the main operator is:

Answer Choices: a. Wedge b. Tilde c. Dot d. Horseshoe e. Triple bar

Answer: d. Horseshoe