Propositional Symbolization notes

Question: Sierra is hearty only if Budweiser is bland, given that both Heineken is balanced and Michelob is complex.

Answer Choices: a. (S ⊃ B) ⊃ (H • M) b. (H • M) ⊃ (S ⊃ B) c. (H ⊃ M) ⊃ (S ⊃ B) d. (S ⊃ B) ⊃ (H ⊃ M) e. (H • M) • (S ⊃ B)

Answer: b. (H • M) ⊃ (S ⊃ B)

Question: Corona is drinkable if Pabst is clean tasting, and Foster’s is refreshing only if Guinness is dark.

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

Answer: a. (P ⊃ C) • (F ⊃ G)

Question: Michelob’s being complex is a necessary condition for Heineken’s being balanced unless Alaskan’s being sweet is a sufficient condition for Carlsberg’s being malty.

Answer Choices: a. (M ⊃ H) ∨ (A ⊃ C) b. (M ⊃ H) ∨ (A ⊃ C) c. (M ≡ H) ∨ (A ≡ C) d. (M ⊃ H) ∨ (A ⊃ C) e. (M ⊃ H) ∨ (A ⊃ C)

Answer: d. (M ⊃ H) ∨ (A ⊃ C)

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

Answer Choices: a. True. b. False.

Answer: a. True.

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

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

Answer: e. Tilde.

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

Answer Choices: a. True. b. False.

Answer: b. False.

Question: In Proposition 2C, the main operator is a:

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

Answer: d. Dot.

Question: Statement 1C is:

Answer Choices: a. Self-contradictory. b. Contingent. c. Consistent. d. Logically equivalent. e. Tautologous.

Answer: e. Tautologous.

Question: The truth table for Statement 1C has how many lines?

Answer Choices: a. Six. b. Eight. c. Four. d. Two. e. Nine.

Answer: c. Four.

Question: Statement 2C is:

Answer Choices: a. Tautologous. b. Contingent. c. Inconsistent. d. Self-contradictory. e. Consistent.

Answer: b. Contingent.

Question: The truth table for Statement 2C has how many lines?

Answer Choices: a. Eight. b. Nine. c. Four. d. Six. e. Twelve.

Answer: a. Eight.

Question: Given the statement: (A ∨ ~S) • (S ⊃ ~A)

Answer Choices: a. Contingent. b. Self-contradictory. c. Inconsistent. d. Valid. e. Tautologous.

Answer: c. Inconsistent.

Question: Given the pair of statements: ~(H ≡ R) and ~(R ⊃ H)

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

Answer: d. Inconsistent.

Question: Given the argument: K ∨ E / E ⊃ ~K // K ≡ ~E

Answer Choices: a. Invalid; fails in 3rd line. b. Invalid; fails in 2nd line. c. Valid. d. Invalid; fails in 4th line. e. Invalid; fails in 1st line.

Answer: b. Invalid; fails in 2nd line.

Question: Given the argument: P ∨ J / ~J ⊃ ~P // J = ~P

Answer Choices: a. Invalid; fails in 3rd line. b. Invalid; fails in 2nd line. c. Invalid; fails in 1st line. d. Valid. e. Invalid; fails in 4th line.

Answer: c. Invalid; fails in 1st line.

Question: Given the argument: C ⊃ M / J ⊃ H // (N • D) ∨ (G • C) / H ∨ M // G • M

Answer Choices: a. Uncogent. b. Cogent. c. Sound. d. Invalid. e. Valid.

Answer: d. Invalid.

Question: Given the argument: W ∨ S / E ∨ ~A / (K ∨ L) ≡ (A • S) // L ⊃ (E • W)

Answer Choices: a. Invalid. b. Uncogent. c. Valid. d. Cogent. e. Sound.

Answer: c. Valid.

Question: Given the statements: R ⊃ (Q ∨ N) / Q ⊃ (U ⊃ B) / B ⊃ (N • U) / R • B

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

Answer: a. Inconsistent.

Question: Given the statements: P ≡ (S ∨ ~A) / A ⊃ (M • J) / J ⊃ (P • S) / J ≡ A

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

Answer: e. Consistent.

Question: ~S ∨ ~T T ~S

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

Answer: b. DS—valid.

Question: ∼𝐻⊃𝐵∼H⊃B𝐵B

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

Answer: a. MT—valid.