Question: If computers can play chess, then they can think. But computers cannot think. Thus, computers cannot play chess.
Answer Choices: a. Disjunctive syllogism. b. Invalid. c. Denying the antecedent. d. Affirming the consequent. e. Modus tollens.
Answer: e. Modus tollens.
Question: If the nuts are stale, then they should not be put into the salad. Thus, the nuts are stale, since they should not be put into the salad.
Answer Choices: a. Modus ponens. b. Denying the antecedent. c. Invalid. d. Affirming the consequent. e. Disjunctive syllogism.
Answer: d. Affirming the consequent.
Question: If dinosaur DNA has deteriorated, then it is impossible to recreate dinosaurs. If dinosaurs perished long ago, then dinosaur DNA has deteriorated. Hence, if dinosaurs perished long ago, then it is impossible to recreate them.
Answer Choices: a. Constructive dilemma. b. Affirming the consequent. c. Pure hypothetical syllogism. d. Modus tollens. e. Invalid.
Answer: c. Pure hypothetical syllogism.
Question: Either we recycle our trash or we will be inundated in garbage. Therefore, we will not be inundated in garbage, since we recycle our trash.
Answer Choices: a. Disjunctive syllogism. b. Destructive dilemma. c. Pure hypothetical syllogism. d. Modus ponens. e. Invalid.
Answer: d. Modus ponens.
Question: Delta advertises a sale and either United lowers fares or American hires pilots.
Answer Choices: a. D • (U ∨ A) b. D ∨ (U • A) c. D ∨ U ∨ A d. (D • U) ∨ A e. D ∨ (U • A)
Answer: a. D • (U ∨ A)
Question: Frontier’s improving service implies that not both Continental buys planes and Southwest expands routes.
Answer Choices: a. F ⊃ ~(C ∨ S) b. F ⊃ ~(C • S) c. F ⊃ ~(C • S) d. (F ⊃ ~C) • S e. F ⊃ ~(C • S)
Answer: c. F ⊃ ~(C • S)
Question: Continental buys planes unless neither Frontier improves service nor United lowers fares.
Answer Choices: a. C ∨ ~(F • U) b. C ∨ ~(F ∨ U) c. C ∨ ~(F ∧ U) d. C ⊃ ~(F ∨ U) e. ~(F ∨ U) ⊃ C
Answer: b. C ∨ ~(F ∨ U)
Question: American’s hiring pilots is a sufficient condition for both Delta’s advertising a sale and Southwest’s expanding routes.
Answer Choices: a. (D • S) ∨ A b. (D ⊃ A) • (S ⊃ A) c. (D ⊃ S) ⊃ A d. A ⊃ (D • S) e. A ≡ (D • S)
Answer: d. A ⊃ (D • S)
Question: Frontier’s improving service is a necessary condition for either Continental’s buying planes or United’s lowering fares.
Answer Choices: a. F ≡ (C ∨ U) b. F ⊃ (C ∨ U) c. (F ⊃ C) • (F ⊃ U) d. (C ∨ U) ⊃ F e. (C ⊃ F) ∨ (F ⊃ U)
Answer: d. (C ∨ U) ⊃ F
Question: Southwest expands routes if either American does not hire pilots or United does not lower fares.
Answer Choices: a. ~(A ∨ U) ⊃ S b. ~(A ⊃ U) ⊃ S c. S ⊃ ~(A ∨ U) d. (S ⊃ ~A) ∨ ~U e. ~(A ∨ U) ⊃ S
Answer: e. ~(A ∨ U) ⊃ S
Question: Continental buys planes if and only if both Delta does not advertise a sale and Southwest does not expand routes.
Answer Choices: a. C ≡ ~(D • S) b. C ⊃ ~(D • ~S) c. C ≡ ~(D • S) d. ~(D ∨ S) ⊃ C e. C ∨ ~(D • ~S)
Answer: c. C ≡ ~(D • S)
Question: United’s lowering fares is a sufficient and necessary condition for American’s hiring pilots, given that Frontier does not improve service.
Answer Choices: a. (U ≡ A) ⊃ ~F b. ~F ⊃ (U ≡ A) c. (F ⊃ U) • (~F ⊃ A) d. (F ≡ U) • (F ≡ A) e. ~F ≡ (U ⊃ A)
Answer: b. ~F ⊃ (U ≡ A)
Question: Continental buys planes if Delta advertises a sale, and Frontier improves service only if Southwest expands routes.
Answer Choices: a. (D ⊃ C) • (F ⊃ S) b. (D ≡ C) • (F ⊃ S) c. (D ⊃ C) • (S ⊃ F) d. (D ⊃ C) • (S ⊃ F) e. (C ⊃ D) • (F ⊃ S)
Answer: a. (D ⊃ C) • (F ⊃ S)
Question: United lowers fares if and only if both Continental buys planes and Delta advertises a sale, provided that American hires pilots.
Answer Choices: a. (U ≡ A) • (C ≡ D) b. A ⊃ [U ≡ (C ≡ D)] c. (U ≡ (C ≡ D)) ⊃ A d. A ≡ [U ⊃ (C ⊃ D) ≡ U] e. (U ⊃ C • D) ⊃ A
Answer: b. A ⊃ [U ≡ (C ≡ D)]
Question: Given that A and B are true and X and Y are false, determine the truth value of Proposition 1H.
Answer Choices: a. True b. False
Answer: b. False
Question: In Proposition 1H, the main operator is a:
Answer Choices: a. Horseshoe b. Tilde c. Dot d. Triple bar e. Wedge
Answer: c. Dot
Question: Given that A and B are true and X and Y are false, determine the truth value of Proposition 2H.
Answer Choices: a. True b. False
Answer: a. True
Question: In Proposition 2H, the main operator is a:
Answer Choices: a. Dot b. Wedge c. Triple bar d. Tilde e. Horseshoe
Answer: e. Horseshoe
Question: Statement 1H is:
Answer Choices: a. Consistent b. Logically equivalent c. Tautologous d. Contingent e. Self-contradictory
Answer: e. Self-contradictory
Question: The truth table for Statement 1H has how many lines?
Answer Choices: a. Two b. Eight c. Four d. Six e. Nine
Answer: c. Four
Question: Statement 2H is:
Answer Choices: a. Inconsistent b. Contingent c. Consistent d. Self-contradictory e. Tautologous
Answer: e. Tautologous
Question: The truth table for Statement 2H has how many lines?
Answer Choices: a. Five b. Nine c. Eight d. Six e. Four
Answer: c. Eight
Question: Given the statement: (E ∨ ~H) • (H ⊃ ~E) This statement is:
Answer Choices: a. Valid b. Self-contradictory c. Tautologous d. Inconsistent e. Contingent
Answer: b. Self-contradictory