Question: Given the following premises: N ∨ C (N ∨ C) ⊃ (F ⊃ ~C) ~C
Answer Choices: a. F ⊃ C, 1, 2, MP b. N, 1, 3, DS c. ~F, 2, 3, MT d. ~N, 1, 3, MT e. ~C • R, 3, Add
Answer: a. F ⊃ C, 1, 2, MP
Question: Given the following premises: (S • J) ∨ (~S ⊃ ~J) S ∨ ~S ~J ⊃ P
Answer Choices: a. S, 2, Taut b. ~J ∨ ~J, 1, 2, CD c. S ≡ J, 1, Equiv d. ~J ∨ P, 3, Impl e. ~J ⊃ P, 3, Trans
Answer: c. S ≡ J, 1, Equiv
Question: Given the following premises: Q ⊃ (A ∨ ~T) T A ∨ ~T
Answer Choices: a. Q ⊃ (~A ∨ ~T), 1, DN b. (A ∨ ~T) ⊃ Q, 1, Com c. (Q ⊃ A) ∨ ~T, 1, Assoc d. Q, 1, 3, MP e. A, 2, 3, DS
Answer: a. Q ⊃ (~A ∨ ~T), 1, DN
Question: Given the following premises: ~E ⊃ P ~P ~(P ∨ ~H)
Answer Choices: a. ~H, 2, 3, DS b. ~P ⊃ ~(P ∨ ~H), 2, 3, Conj c. ~P ⊃ H, 3, DM d. E, 1, 2, MT e. ~P ⊃ E, 1, Trans
Answer: b. ~P ⊃ ~(P ∨ ~H), 2, 3, Conj
Question: Given the following premises: ~N K ⊃ ~N ~N ∨ (K • S)
Answer Choices: a. (~N ∨ K) • S, 3, Assoc b. K, 1, 2, MT c. N ⊃ ~K, 2, Trans d. K • S, 1, 3, DS e. (~N • K) ∨ (~N • S), 3, Dist
Answer: d. K • S, 1, 3, DS
Question: Given the following premises: Q ⊃ (H • ~F) ~Q ⊃ ~M ~G ⊃ (Q • ~M)
Answer Choices: a. G ∨ (Q • ~M), 2, Add b. Q, 2, Simp c. ~Q ∨ ~~M, 2, DM d. Q ⊃ (~H ∨ F), 1, DM e. G, 2, 3, MT
Answer: c. ~Q ∨ ~~M, 2, DM
Question: Given the following premises: (S ⊃ R) ⊃ (J ⊃ T) (P ⊃ R) ⊃ (S ⊃ R) R ⊃ J
Answer Choices: a. (P ⊃ R) ⊃ (J ⊃ T), 1, 2, HS b. S ⊃ J, 1, 3, HS c. P ⊃ J, 2, 3, HS d. (S ⊃ R) • (P ⊃ R), 1, 2, Conj e. R ⊃ T, 1, 3, HS
Answer: a. (P ⊃ R) ⊃ (J ⊃ T), 1, 2, HS
Question: Given the following premises: Q ⊃ (H • L) H ⊃ ~Q L ⊃ ~Q
Answer Choices: a. (Q ⊃ H) ⊃ L, 1, Exp b. L ⊃ (H • L), 1, 3, HS c. Q ⊃ ~Q, 1, 3, HS d. H ⊃ L, 2, 3, HS e. (L ⊃ Q) • (H ⊃ ~Q), 2, 3, Conj
Answer: e. (L ⊃ Q) • (H ⊃ ~Q), 2, 3, Conj
Question: Given the following premises: F ⊃ J A ⊃ (F • J) A • (Q ∨ N)
Answer Choices: a. J ⊃ F, 1, Com b. A • (N ∨ Q), 3, Com c. A ⊃ J, 1, 2, HS d. (A ⊃ F) • (A ⊃ J), 2, Dist e. (A • Q) ∨ N, 3, Assoc
Answer: b. A • (N ∨ Q), 3, Com
Question: Given the following premises: D ∨ ~T D ∨ (~T ⊃ ~R) D
Answer Choices: a. (D ∨ ~T) • (D ∨ ~R), 2, Dist b. D ∨ ~T ⊃ R, 2, Assoc c. D ∨ T, 1, DN d. ~T, 1, 3, DS e. ~T ⊃ ~R, 2, 3, DS
Answer: a. (D ∨ ~T) • (D ∨ ~R), 2, Dist
Question: Given the following premises: (C ⊃ ~F) ⊃ E G ∨ (C ⊃ ~F) ~(C ⊃ ~F)
Answer Choices: a. G ⊃ E, 1, 2, HS b. C, 1, Simp c. C ⊃ (~F ⊃ E), 1, Exp d. G ∨ C ⊃ ~F, 2, Assoc e. G, 2, 3, DS
Answer: c. C ⊃ (~F ⊃ E), 1, Exp
Question: Given the following premises: K ∨ ~H K ∨ (~H ⊃ B ⊃ J) J ⊃ D
Answer Choices: a. H ⊃ K, 1, Impl b. B ⊃ D, 2, 3, HS c. K, 1, Simp
Answer: c. K, 1, Simp
Question: Given the following premises: R ⊃ ~S R ⊃ (~S ⊃ ~F) ~S ⊃ (F • N)
Answer Choices: a. (~S • F) ⊃ N, 3, Exp b. ~S, 1, Simp c. F • N, 1, 3, MP d. R ⊃ (~S ∨ ~F), 2, DM e. (~S • F) ⊃ (~S ⊃ N), 3, Dist
Answer: d. R ⊃ (~S ∨ ~F), 2, DM
Question: Given the following premises: ~T ⊃ E ~K ⊃ (~T ∨ ~L) M ⊃ (~K ∨ L)
Answer Choices: a. (M ⊃ ~K) ∨ L, 3, Assoc b. M ⊃ (~K ∨ L), 3, Impl c. M ⊃ (~K ∨ L), 3, DN d. ~K ⊃ T, 2, Taut e. ~K ⊃ E, 1, 2, HS
Answer: b. M ⊃ (~K ∨ L), 3, Impl
Question: Given the following premises: ~R ∨ ~R R ∨ (~J ⊃ H) ~R ⊃ (H • B)
Answer Choices: a. ~J ⊃ H, 1, 2, DS b. R, 1, DN c. R ∨ (~J ⊃ H), 2, Assoc d. R ⊃ ~J ⊃ H, 2, Assoc e. H • B, 1, 3, MP
Answer: c. R ∨ (~J ⊃ H), 2, Assoc
Question: Given the following premises: (F • ~M) ⊃ (L • ~G) P ⊃ L ~(L • ~G)
Answer Choices: a. ~(F • ~M), 1, 3, MT b. ~L, 3, Simp c. ~P, 2, 3, MT d. ~L ∨ G, 3, DM e. L ⊃ P, 2, Trans
Answer: a. ~(F • ~M), 1, 3, MT
Question: Given the following premises: ~P L ⊃ (P ∨ M) (P • M) ⊃ (~R ∨ ~R)
Answer Choices: a. (P • M) ⊃ ~R, 3, Taut b. P, 3, Simp c. L ⊃ (~R ∨ ~R), 2, 3, HS d. (L ⊃ P) ∨ (L ⊃ M), 2, Dist e. M, 1, 2, DS
Answer: a. (P • M) ⊃ ~R, 3, Taut