b. D ⊃ [(H ⊃ R) ⊃ W]
c. [(H ∨ R) ⊃ D] ⊃ W
d. D ⊃ [(H ∨ R) ⊃ W]
e. D ⊃ (H ∨ R) ⊃ W
7. Princess and Azmara improve gym facilities only if neither Carnival controls rowdiness nor Seabourn reduces fares.
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)
8. 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.
a. (R ⊃ D) ≡ (C ⊃ W)
b. (D ⊃ W) ≡ (R ⊃ C)
c. (D ⊃ R) ≡ (W ⊃ C)
d. (D ⊃ R) ∨ (W ⊃ C)
e. (R ≡ D) ⊃ (W ≡ C)
9. 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.
a. (P ⊃ C) ⊃ [(A ⊃ N) • (A ⊃ C)]
b. (P ≡ C) ⊃ [A ⊃ (N • H)]
c. [A ≡ (N • H)] ⊃ (P ⊃ C)
d. [(A ⊃ N) • (A ⊃C)] ⊃ (P ⊃ C)
e. (P ⊃ C) ⊃ [A ≡ (N • H)]
10. 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.
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)]
Proposition 1B
Given the following proposition:
∼[(A ∨ ∼ B) ⊃ X] ⊃ [∼ Y ⊃ (A • X)]
11. Given that A and B are true and X and Y are false, determine the truth value of Proposition 1B.
a. True.