Venn Diagrams questions

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

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

Answer: b. Four

Question: The truth table for Statement 3A has how many lines?

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

Answer: b. Eight

Question: Princess drops its dress codes or Oceania enlarges its fleet, and Seabourn reduces its fares.

Answer Choices: a. P • (O ∨ S) b. (P • O) ∨ S c. P ∨ (O • S) d. P ∨ O • S e. (P ∨ O) • S

Answer: e. (P ∨ O) • S

Question: Not either Regent enlarges its casinos or Celebrity revises its itineraries if Holland remodels its staterooms.

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

Answer: a. H ⊃ ~(R ∨ C)

Question: Norwegian improves its entertainment only if both Disney does not promote family cruises and Windstar does not diversify its activities.

Answer Choices: a. N ⊃ (~D ∨ ~W) b. N ⊃ (~D • ~W) c. (~D • ~W) ⊃ N d. N ⊃ (~D • W) e. ~D • W ⊃ N

Answer: b. N ⊃ (~D • ~W)

Question: Either Azmara or Seabourn do not open new boutiques provided that Princess improves its cuisine.

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

Answer: a. P ⊃ (~A ∨ ~S)

Question: Carnival advertises its parties if and only if Disney’s promoting family cruises implies that Norwegian improves its entertainment.

Answer Choices: a. (C ⊃ D) ⊃ N b. (C ≡ D) • (N ⊃ C) c. C ≡ (D ⊃ N) d. C ⊃ (D ≡ N) e. C ≡ (N ⊃ D)

Answer: c. C ≡ (D ⊃ N)

Question: If Disney promotes family cruises, then if either Holland remodels its staterooms or Regent enlarges its casinos, then Windstar diversifies its activities.

Answer Choices: a. D ⊃ [(H ∨ R) ⊃ W] b. D ⊃ [(H ⊃ R) ⊃ W] c. D ⊃ (H ⊃ R) ∨ W d. D ⊃ [(H ∨ R) ⊃ W] e. D ⊃ [(H ∨ R) ⊃ W]

Answer: d. D ⊃ [(H ∨ R) ⊃ W]

Question: Princess and Azmara improve gym facilities only if neither Carnival controls rowdiness nor Seabourn reduces fares.

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

Answer: b. (P • A) ⊃ (~C ∨ S)

Question: Regent’s enlarging its casinos is a necessary condition for Disney’s offering games if and only if Windstar’s diversifying its activities is a sufficient condition for Costa’s enlarging its nightspots.

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

Answer: c. (R ⊃ D) ≡ (W ⊃ C)

Question: Azmara’s opening new boutiques is a sufficient and necessary condition for both Norwegian’s improving entertainment and Holland’s remodeling its staterooms if Princess’s dropping its dress codes implies that Celebrity revises its itineraries.

Answer Choices: a. (P ⊃ C) ⊃ [(A ⊃ N) • (A ⊃ C)] b. (P ⊃ C) ⊃ [A ⊃ (N • H)] c. [(A ≡ N) • (A ⊃ C)] ⊃ P d. [(A ⊃ N) • (A • C)] ⊃ (P ⊃ C) e. (P ⊃ C) ⊃ [A ≡ (N • H)]

Answer: e. (P ⊃ C) ⊃ [A ≡ (N • H)]

Question: Seabourn revises its menu given that Norwegian and Princess halt tipping, unless Oceania enlarges its fleet if and only if both Costa improves its gym facilities and Regent enlarges its casinos.

Answer Choices: a. [S ⊃ (N • P)] ∨ [O ⊃ (C • R)] b. [(N • P) ≡ S] ∨ [O ⊃ (C • R)] c. [(N • P) ≡ S] ∨ [O ≡ (C • R)] d. [S ⊃ (N • P)] ⊃ [O ⊃ (C • R)] e. [S ⊃ (N • P)] ≡ [O ∨ (C • R)]

Answer: c. [(N • P) ≡ S] ∨ [O ≡ (C • R)]

Question: Coors is smooth or both Beck’s is subtle and Guinness is heavy.

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

Answer: a. C ∨ (B • G)

Question: Budweiser is bland if either Heineken is balanced or Foster’s is refreshing.

Answer Choices: a. (H ⊃ B) ∨ F b. (B ⊃ H) ∨ F c. B ⊃ (H ∨ F) d. B ⊃ H ∨ F e. (H ∨ F) ⊃ B

Answer: e. (H ∨ F) ⊃ B

Question: Alaskan is sweet only if neither Heineken is balanced nor Pabst is clean tasting.

Answer Choices: a. A ⊃ ∼ (H ∨ ∼ P) b. A ⊃ ∼ H • ∼ P c. ∼ (H ∨ P) ⊃ A d. A ⊃ (H ∨ P) e. ∼ (H ∨ ∼ P) ⊃ A

Answer: d. A ⊃ ∼ (H ∨ ∼ P)

Question: Sierra is hearty given that Michelob’s being flavorful implies that Guinness is heavy.

Answer Choices: a. (S ⊃ M) ⊃ G b. (G ⊃ M) ⊃ S c. S ⊃ (M ⊃ G) d. M ⊃ (G ⊃ S) e. (M ⊃ G) ⊃ S

Answer: e. (M ⊃ G) ⊃ S

Question: Harp is soothing if and only if both Miller is not zesty and Coors is not smooth.

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

Answer: c. H ≡ ∼ (M • ∼ C)