Question: (K ⊃ ~A) • (S ⊃ ~D) A ∨ D ∴ ~K ∨ ~S
Answer Choices: a. Invalid b. Modus tollens c. Affirming the consequent d. Denying the antecedent e. Destructive dilemma
Answer: e. Destructive dilemma
Question: In the expression ‘P ∨ Q’, ‘P’ is called:
Answer Choices: a. A disjunction b. A conjunct c. A disjunct d. A conjunction e. An antecedent
Answer: c. A disjunct
Question: According to De Morgan’s rule, ~(P ∨ Q) is logically equivalent to:
Answer Choices: a. P ∨ Q b. ~P ∨ ~Q c. P • Q d. ~P • ~Q e. P ≡ Q
Answer: d. ~P • ~Q
Question: If an indirect truth table requiring more than one line is constructed for either an argument or a series of statements and no contradiction is derived on the first line, then:
Answer Choices: a. The argument is valid and the statements are consistent. b. The argument is invalid and the statements are consistent. c. The argument is valid and the statements are inconsistent. d. The argument is invalid and the statements are inconsistent. e. The second line of the truth table must be completed.
Answer: b. The argument is invalid and the statements are consistent.
Question: If a group of statements are inconsistent, this means:
Answer Choices: a. It is not possible for all of them to be true. b. All of them are false. c. At least one of them is false. d. It is possible for all of them to be false. e. Exactly one of them is false.
Answer: a. It is not possible for all of them to be true.
Question: The dot operator is used to translate:
Answer Choices: a. “Either.” b. “Unless.” c. “Implies.” d. “Provided that.” e. “Moreover.”
Answer: e. “Moreover.”
Question: Suppose an indirect truth table is constructed for an argument, and the truth table requires more than one line. If no contradiction is obtained on the first line, then:
Answer Choices: a. The argument is valid. b. The argument could still be valid. c. The argument is invalid. d. The argument is consistent. e. The argument is sound.
Answer: c. The argument is invalid.
Question: Suppose an indirect truth table is constructed for a series of statements, and the truth table requires more than one line. If a contradiction is reached on the first line, then:
Answer Choices: a. The statements are consistent. b. The statements are contingent. c. The statements are inconsistent. d. The statements could still be invalid. e. The second line in the truth table must be completed.
Answer: e. The second line in the truth table must be completed.
Question: Hertz runs a sale or both Avis buys new cars and Budget lowers rates.
Answer Choices: a. H ∨ A • B b. H ∨ (A • B) c. (H ∨ A) • B d. H • (A ∨ B) e. H • A ∨ B
Answer: b. H ∨ (A • B)
Question: Thrifty lays off workers only if neither National improves efficiency nor Enterprise reorganizes.
Answer Choices: a. T ⊃ ~(N ∨ E) b. ~(N ∨ E) ⊃ T c. T ⊃ ~(N ∨ ~T) d. (N ∨ ~E) ⊃ T e. T ≡ ~(N ∨ E)
Answer: a. T ⊃ ~(N ∨ E)
Question: Budget lowers rates unless Hertz and Thrifty do not overhaul operations.
Answer Choices: a. B ∨ ~(H • T) b. B ∨ ~(H • ~T) c. B ⊃ ~(H • ~T) d. ~(H • ~T) ⊃ B e. (B ∨ ~H) • ~T
Answer: a. B ∨ ~(H • T)
Question: If National’s improving efficiency implies that Enterprise reorganizes, then Avis buys new cars.
Answer Choices: a. (N ⊃ E) ⊃ A b. N ⊃ (E ⊃ A) c. (N ⊃ E) ⊃ A d. A ⊃ (N ⊃ E) e. (E ≡ N) ⊃ A
Answer: c. (N ⊃ E) ⊃ A
Question: Not both Hertz runs a sale and Thrifty lays off workers if either Avis buys new cars or Budget lowers rates.
Answer Choices: a. ~(H • T) ⊃ (A ∨ B) b. (A ∨ B) ⊃ ~(H • T) c. ~(H • T) ⊃ (A ∨ B) d. (A ∨ B) ⊃ ~(H • T) e. (A • B) ⊃ ~(H ∨ T)
Answer: d. (A ∨ B) ⊃ ~(H • T)
Question: National does not improve efficiency or Enterprise does not reorganize, given that Thrifty lays off workers.
Answer Choices: a. T ⊃ ~(N ∨ E) b. ~(N ∨ E) ⊃ T c. ~(N ∨ E) ⊃ T d. (T ⊃ N) ∨ ~E e. T ⊃ ~(N ∨ ~E)
Answer: e. T ⊃ ~(N ∨ ~E)
Question: Budget’s lowering rates implies that Hertz runs a sale, only if Avis does not buy new cars.
Answer Choices: a. (B ⊃ H) ⊃ ~A b. ~A ⊃ (B ⊃ H) c. (B ⊃ H) ≡ ~A d. (H ⊃ B) ⊃ ~A e. (B ⊃ H) ⊃ A
Answer: a. (B ⊃ H) ⊃ ~A
Question: Thrifty’s laying off workers is a sufficient condition for National’s improving efficiency, if Enterprise reorganizes.
Answer Choices: a. E ⊃ (N ⊃ T) b. (T ⊃ N) ⊃ E c. E ⊃ (T ⊃ N) d. (N ⊃ E) ⊃ T e. E ⊃ (T ⊃ N)
Answer: c. E ⊃ (T ⊃ N)
Question: Hertz’s running a sale and Budget’s lowering rates are a necessary condition for either Avis’s buying new cars or Thrifty’s laying off workers.
Answer Choices: a. (A ∨ T) ⊃ (H • B) b. (H • B) ⊃ (A ∨ T) c. (H ∨ B) ⊃ (A ∨ T) d. (A ∨ T) ⊃ (H • B) e. (H • B) ⊃ (A ∨ T)
Answer: d. (A ∨ T) ⊃ (H • B)