Argument Construction solved questions

Question: R R ⊃ ~D ∴ ~D

Answer Choices: a. Invalid b. Affirming the consequent c. Disjunctive syllogism d. Modus tollens e. Modus ponens

Answer: e. Modus ponens

Question: S ⊃ ~C ∴ ~C ∴ S

Answer Choices: a. Modus tollens b. Affirming the consequent c. Denying the antecedent

Answer: c. Denying the antecedent

Question: (~W ⊃ L) • (N ⊃ ~R) N ∨ ~W ∴ L ∨ ~R

Answer Choices: a. Invalid b. Pure hypothetical syllogism c. Destructive dilemma d. Denying the antecedent e. Constructive dilemma

Answer: e. Constructive dilemma

Question: E ⊃ ~T ~N ⊃ E ∴ ~N ⊃ ~T

Answer Choices: a. Modus ponens b. Constructive dilemma c. Pure hypothetical syllogism d. Invalid e. Disjunctive syllogism

Answer: c. Pure hypothetical syllogism

Question: ~F ⊃ L ∴ F ∴ ~L

Answer Choices: a. Denying the antecedent b. Modus ponens c. Affirming the consequent d. Modus tollens e. Invalid

Answer: a. Denying the antecedent

Question: In the expression P • Q, ‘P’ is called:

Answer Choices: a. A conjunction b. A disjunct c. An antecedent d. A conjunct e. A disjunction

Answer: d. A conjunct

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

Answer: c. ~P • ~Q

Question: If a group of statements are consistent, this means:

Answer Choices: a. At least one of them is true. b. It is possible for all of them to be true. c. At least one of them is false. d. All of them are true. e. It is possible for all of them to be false.

Answer: b. It is possible for all of them to be true.

Question: If an indirect truth table requiring more than one line is constructed for either an argument or a series of statements and a contradiction is derived on the first line, then:

Answer Choices: a. The second line must be completed. b. The argument is valid and the statements are consistent. c. The argument is valid and the statements are inconsistent. d. The argument is invalid and the statements are consistent. e. The argument is invalid and the statements are inconsistent.

Answer: a. The second line must be completed.

Question: The wedge operator is used to translate:

Answer Choices: a. “Nevertheless.” b. “Moreover.” c. “Unless.” d. “Implies.” e. “Provided that.”

Answer: c. “Unless.”

Question: A few flights are available.

Answer Choices: a. Some flights are available. b. Some flights are things that are available. c. Some flights are things that are available and some flights are not things that are available. d. Some flights are not things that are available. e. All flights are not available.

Answer: b. Some flights are things that are available.

Question: Given the following premises: ~R ≡ ~R N • ~T R ⊃ ~(N • ~T)

Answer Choices: a. ~T, 2, Simp b. (N • ~T) ⊃ ~R, 3, Trans c. ~R, 2, 3, MT d. R ⊃ (~N ∨ ~~T), 3, DM e. ~R, 1, Taut

Answer: d. R ⊃ (~N ∨ ~~T), 3, DM

Question: Given the following premises: G ⊃ ~A K ⊃ (G ⊃ ~A) G ⊃ M

Answer Choices: a. (K ⊃ G) ⊃ ~A, 2, Exp b. K ⊃ (~A ⊃ G), 2, Com c. (K ⊃ G) • ~A, 2, Assoc d. K, 1, 2, MP e. M, 1, 3, MP

Answer: b. K ⊃ (~A ⊃ G), 2, Com

Question: Given the following premises: ~(Q ⊃ ~S) ~F ⊃ (Q ⊃ ~S) H ∨ (Q ⊃ ~S)

Answer Choices: a. (H • Q) ∨ (H ⊃ ~S), 3, Dist b. ~Q ∨ S, 1, DM c. F, 1, 2, MT d. H, 1, 3, DS e. ~F, 1, 2, MT

Answer: e. ~F, 1, 2, MT

Question: Given the following premises: N R ⊃ ~N ~C • (T ⊃ R)

Answer Choices: a. ~C, 3, Simp b. T ⊃ ~N, 2, 3, HS c. (~C • T) ⊃ R, 3, Assoc d. ~R, 1, 2, MT e. N ⊃ ~R, 2, Trans

Answer: a. ~C, 3, Simp

Question: Given the following premises: (K • ~T) ∨ (K ⊃ ~H) ~M ⊃ (K ⊃ ~H) ~(K ⊃ ~H)

Answer Choices: a. ~K ∨ H, 3, DM b. K ⊃ ~T, 1, 3, DS c. K • (~T ∨ ~H), 1, Dist d. ~M, 2, 3, MT e. (~M • K) ⊃ ~H, 2, Exp

Answer: c. K • (~T ∨ ~H), 1, Dist

Question: Given the following premises: A G ⊃ (A ⊃ ~L) ~A ∨ ~G

Answer Choices: a. A ∨ G, 3, DN b. G ⊃ (A ⊃ ~L), 2, Assoc c. ~L, 1, 2, MP d. ~G, 1, 3, DS e. G ⊃ (~L ⊃ ~A), 2, Trans

Answer: e. G ⊃ (~L ⊃ ~A), 2, Trans

Question: Given the following premises: (S ⊃ ~F) • (~F ⊃ B) S ∨ ~F ~F

Answer Choices: a. S ⊃ B, 1, HS b. ~F ⊃ B, 1, 2, CD c. S, 2, 3, DS d. B, 1, 3, MP e. ~S, 1, 3, MT

Answer: b. ~F ⊃ B, 1, 2, CD

Question: Given the following premises: N ≡ R (N ⊃ R) ⊃ C N

Answer Choices: a. (N ⊃ R) ∨ (R ⊃ N), 1, Equiv b. N • (R ⊃ C), 2, Assoc c. C ⊃ (N ⊃ R), 2, Com

Answer: a. (N ⊃ R) ∨ (R ⊃ N), 1, Equiv

Question: Given the following premises: ~M ⊃ S ~M (M ∨ H) ∨ ~S

Answer Choices: a. H, 2, 3, DS b. M ∨ H, 3, Simp c. M ∨ (H ∨ ~S), 3, Assoc d. ~S, 1, 2, MP e. M ∨ S, 1, Impl

Answer: c. M ∨ (H ∨ ~S), 3, Assoc

Question: Given the following premises: (J • ~N) ∨ T (~J ⊃ ~N) ~T

Answer Choices: a. T, 1, 2, DS b. ~J ∨ N, 2, DM c. J ⊃ ~N, 1, 3, DS d. J ⊃ (~N ∨ T), 1, Assoc e. ~J, 2, Simp

Answer: a. T, 1, 2, DS

Question: Given the following premises: ~U ⊃ (S • K) R ⊃ (~U ∨ ~U) S ≡ ~U

Answer Choices: a. (~U • S) ⊃ K, 1, Exp b. R ⊃ U, 2, DN c. R ⊃ ~U, 2, Taut d. R ⊃ (S • K), 1, 2, HS e. (S ⊃ U) ⊃ (~U ⊃ ~S), 3, Equiv

Answer: c. R ⊃ ~U, 2, Taut