Propositional Symbolization test

Question: Either Safeco reduces premiums and Geico cuts costs or Farmers hires agents.

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

Answer: c

Question: Not both Travelers and Conseco run an ad if Liberty opens new offices.

Answer Choices: a. L ⊃ ~(T • C) b. ~[C ⊃ (L ⊃ C)] c. L ⊃ (~T ⊃ ~C) d. ~(T • C) ⊃ L e. (~T ⊃ ~C) ⊃ L

Answer: a

Question: Progressive increases its territory if neither Safeco cuts costs nor Travelers runs an ad.

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

Answer: d

Question: If either Nationwide or Geico does not open new offices, then Metropolitan does not hire agents.

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

Answer: a

Question: Progressive expands coverage if and only if both Liberty and Conseco do not cut costs.

Answer Choices: a. (~L • ~C) ⊃ P b. P ≡ (~L • ~C) c. P ≡ ~(L • ~C) d. P ≡ ~(L ∨ C) e. P ≡ (L • ~C)

Answer: b

Question: Metropolitan’s reorganizing implies that Allstate hires agents, provided that Liberty reduces premiums.

Answer Choices: a. M ⊃ (L ⊃ A) b. L ⊃ (A ⊃ M) c. (L ⊃ M) ⊃ A d. M ⊃ (A ⊃ L) e. L ⊃ (M ⊃ A)

Answer: e

Question: Either Safeco reduces premiums and Geico cuts costs or Farmers hires agents.

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

Answer: c. (S ∨ G) • F

Question: Not both Travelers and Conseco run an ad if Liberty opens new offices.

Answer Choices: a. L ⊃ ~(T • C) b. ~[C • (L ⊃ C)] c. L ⊃ ~(T • ~C) d. ~(T • C) ⊃ L e. (~T • ~C) ⊃ L

Answer: a. L ⊃ ~(T • C)

Question: Progressive increases its territory if neither Safeco cuts costs nor Travelers runs an ad.

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

Answer: d. ~(S ∨ T) ⊃ P

Question: If either Nationwide or Geico does not open new offices, then Metropolitan does not hire agents.

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

Answer: a. (~N ∨ ~G) ⊃ ~M

Question: Progressive expands coverage if and only if both Liberty and Conseco do not cut costs.

Answer Choices: a. (~L • ~C) ⊃ P b. P ≡ (~L • ~C) c. P ≡ (~L ⊃ C) d. P ≡ (~L ∨ ~C) e. (L ≡ A) ∨ ~S

Answer: b. P ≡ (~L • ~C)

Question: Metropolitan’s reorganizing implies that Allstate hires agents, provided that Liberty reduces premiums.

Answer Choices: a. M ⊃ (L ⊃ A) b. L ⊃ (A ⊃ M) c. (L ⊃ M) ⊃ A d. M ⊃ (A ⊃ L) e. L ⊃ (M ⊃ A)

Answer: e. L ⊃ (M ⊃ A)

Question: Either Safeco reduces premiums and Geico cuts costs or Farmers hires agents.

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

Answer: c. (S ∨ G) • F

Question: Not both Travelers and Conseco run an ad if Liberty opens new offices.

Answer Choices: a. L ⊃ ~(T • C) b. ~(L ⊃ (T • C)) c. L ⊃ (~T • ~C) d. ~(T • C) ⊃ L e. (~T • ~C) ⊃ L

Answer: a. L ⊃ ~(T • C)

Question: Progressive increases its territory if neither Safeco cuts costs nor Travelers runs an ad.

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

Answer: d. ~(S ∨ T) ⊃ P

Question: If either Nationwide or Geico does not open new offices, then Metropolitan does not hire agents.

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

Answer: a. ~(N ∨ ~G) ⊃ ~M

Question: Progressive expands coverage if and only if both Liberty and Conseco do not cut costs.

Answer Choices: a. (~L • ~C) ⊃ P b. P ≡ (~L • ~C) c. P ≡ ~(L • ~C) d. P ≡ ~(L ∨ ~C) e. (L ≡ C) ⊃ ~P

Answer: b. P ≡ (~L • ~C)

Question: Metropolitan’s reorganizing implies that Allstate hires agents, provided that Liberty reduces premiums.

Answer Choices: a. M ⊃ (L ⊃ A) b. L ⊃ (A ⊃ M) c. L ⊃ A d. M ⊃ (A ⊃ L) e. L ⊃ (M ⊃ A)

Answer: e. L ⊃ (M ⊃ A) Question: M H ⊃ ~M ~H Answer Options: a. Invalid b. MT—valid c. MP—valid d. DS—valid e. DA—invalid Correct Answer: b. MT—valid

Question: ~N ⊃ H H ~N

Answer Choices: a. DA—invalid b. DS—valid c. MP—valid d. MT—valid e. AC—invalid

Answer: e. AC—invalid

Question: (~M ⊃ E) • (K ⊃ ~C) K ∨ ~M

Answer Choices: a. HS—valid b. CD—valid c. DD—valid d. MP—valid e. Invalid

Answer: b. CD—valid

Question: ~T ⊃ F ~F ⊃ G ~T ⊃ G

Answer Choices: a. Invalid b. CD—valid c. HS—valid d. CD—invalid e. DA—invalid

Answer: a. Invalid

Question: ~A ⊃ ~F C ⊃ ~A C ⊃ ~F

Answer Choices: a. MT—valid b. CD—valid c. Invalid d. DD—invalid

Answer: a. MT—valid Question 493: Either Fiat improves mileage and Toyota closes a factory or Honda reduces inventory. Answer Options: a. F • (T ∨ H) b. F ∨ T ∨ H c. (F ∨ T) ∨ H d. (F ∨ T) ∨ H e. F ∨ T • H Correct Answer: D

Question: If Chrysler increases sales, then it is not the case that both Mercedes introduces a new model and Nissan lays off workers.

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

Answer: C

Question: If Nissan lays off workers, then if Toyota closes a factory, then neither Honda nor Fiat reduces inventory.

Answer Choices: a. N ⊃ [T ⊃ ~(H ∨ F)] b. N ⊃ T ⊃ ~(H ∨ F) c. N ⊃ T ⊃ (H ∨ F) d. (N ⊃ T) ⊃ ~(H ∨ F)

Answer: A