Propositional Symbolization study guide

Question: ∼𝐵⊃𝐽∼B⊃J∼𝐽∼J∼𝐵∼B

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

Answer: b. AC—invalid.

Question: D v M (M ⊃ A) • (D ⊃ C) A v C

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

Answer: e. CD—valid.

Question: K ⊃ R E ≡ R K ⊃ E

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

Answer: c. Invalid.

Question: F ⊃ K∼𝑁⊃𝐹∼N⊃F∼𝑁⊃∼𝐾∼N⊃∼K

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

Answer: b. HS—valid.

Question: P v G(H ⊃ P) • (C ⊃ G)H v ∼𝐶∼C

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

Answer: d. DD—valid.

Question: G ⊃ R∼𝑅∼RG

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

Answer: b. MP—valid.

Question: ∼𝐸⊃∼𝐻∼E⊃∼H∼𝐻∼H∼𝐸∼E

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

Answer: a. Invalid.

Question: ∼𝑄⊃𝑅∼Q⊃RQR

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

Answer: e. DA—invalid.

Question: Amherst reduces class size, and either Williams increases enrollment or Smith raises tuition.

Answer Choices: a. A • (W ⊃ S) b. A • (W ∨ S) c. (A • W) ∨ S d. A ⊃ (W ∨ S) e. A ∨ (W • S)

Answer: b. A • (W ∨ S)

Question: If Williams increases enrollment, then not both Fordham and Georgetown expand course offerings.

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

Answer: e. W ⊃ ~(F • G)

Question: Rice hires new faculty only if neither Duke nor Tulane increases student aid.

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

Answer: c. R ⊃ ~(D ∨ T)

Question: Both Baylor and Rice do not raise tuition provided that Smith increases enrollment.

Answer Choices: a. S ⊃ ~(B • R) b. (~B • ~R) ⊃ S c. (~B ⊃ ~R) ⊃ S d. S ⊃ (B • R) e. ~(B • R) ⊃ S

Answer: a. S ⊃ ~(B • R)

Question: Williams offers new scholarships if and only if either Amherst reduces class size or Smith does not hire new faculty.

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

Answer: d. W ≡ (A ∨ ~S)

Question: Given that A and B are true and X and Y are false, determine the truth value of Proposition 1D.

Answer Choices: a. True. b. False.

Answer: a. True.

Question: In Proposition 1D, the main operator is a:

Answer Choices: a. Tilde. b. Wedge. c. Horseshoe. d. Dot. e. Triple bar.

Answer: e. Triple bar.

Question: Given that A and B are true and X and Y are false, determine the truth value of Proposition 2D.

Answer Choices: a. True. b. False.

Answer: b. False.

Question: Given the statements: 𝑁⊃(𝐿⋅𝑆)N⊃(L⋅S) / 𝑆∨𝐸⊃𝐵S∨E⊃B / 𝐺⊃𝐵G⊃B / 𝐺⊃𝑁G⊃N

Answer Choices: a. Consistent. b. Invalid. c. Tautologous. d. Logically equivalent. e. Inconsistent.

Answer: a. Consistent.

Question: Given the statements: 𝑅⊃𝑀/𝐶⊃𝐸/𝑀⊃∼𝐸/𝑅⋅𝐶R⊃M/C⊃E/M⊃∼E/R⋅C

Answer Choices: a. Contradictory. b. Tautologous. c. Valid. d. Inconsistent. e. Consistent.

Answer: d. Inconsistent.

Question: ∼𝐸⊃𝐿∼E⊃L

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

Answer: e. Invalid.

Question: Redbook increases circulation or both Glamour hires models and Cosmo raises its price.

Answer Choices: a. R ∨ G • C b. R ⊃ (G • C) c. R • (G ∨ C) d. (G • C) ⊃ R e. R ∨ (G • C)

Answer: e. R ∨ (G • C)

Question: If Time expands coverage, then neither Money hires new writers nor Forbes solicits new advertisers.

Answer Choices: a. T ⊃ ~(M ∨ F) b. T ⊃ ~(M ∨ F) c. T ⊃ ~(M ∨ ~F) d. T ⊃ (M ⊃ F) e. ~(M ∨ F) ⊃ T

Answer: b. T ⊃ ~(M ∨ F)

Question: People raises its price only if either Time expands coverage or Newsweek does not increase circulation.

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

Answer: d. P ⊃ (T ∨ ~N)