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INSTRUCTIONS: Select the correct translation for each problem.
1. Princess drops its dress codes or Oceania enlarges its fleet, and Seabourn reduces its fares.
a. P • (O ∨ S)
b. (P • O) ∨ S
c. P ∨ (O • S)
d. P ∨ O • S
e. (P ∨ O) • S
2. Not either Regent enlarges its casinos or Celebrity revises its itineraries if Holland remodels its staterooms.
a. H ⊃ ∼(R ∨ C)
b. H ≡ (∼R ∨ C)
c. ∼ (R ∨ C) ⊃ H
d. (∼R ∨ ∼C) ⊃ H
e. H ⊃ (∼R ∨ ∼C)
3. Norwegian improves its entertainment only if both Disney does not promote family cruises and Windstar does not
diversify its activities.
a. N ⊃ (∼D ∨ ∼W)
b. N ⊃ (∼D • ∼W)
c. (∼D • ∼W) ⊃ N
d. N ⊃ ∼(D • W)
e. ∼(D • W) ⊃ N
4. Either Azmara or Seabourn do not open new boutiques provided that Princess improves its cuisine.
a. P ⊃ (∼A ∨ ∼S)
b. (∼A ∨ ∼S) ⊃ P
c. (∼A • ∼S) ⊃ P
d. P ⊃ ∼(A • S)
e. ∼(A • S) ⊃ P
5. Carnival advertises its parties if and only if Disney’s promoting family cruises implies that Norwegian improves its
entertainment.
a. (C ≡ D) ⊃ N
b. (C ⊃ D) • (N ⊃ C)
c. C ≡ (D ⊃ N)
d. C ⊃ (D ≡ N)
e. C ≡ (N ⊃ D)
6. If Disney promotes family cruises, then if either Holland remodels its staterooms or Regent enlarges its casinos, then
Windstar diversifies its activities.
a. [D ⊃ (H ∨ R)] ⊃ W
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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.
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b. False.
12. In Proposition 1B, the main operator is a:
a. Dot.
b. Triple bar.
c. Wedge.
d. Tilde.
e. Horseshoe.
Proposition 2B
Given the following proposition:
[(A ⊃ Y) ≡ (B ⊃ ∼X)] ∨ ∼[(B • ∼ X) ≡ (Y • A)]
13. Given that A and B are true and X and Y are false, determine the truth value of Proposition 2B.
a. True.
b. False.
14. In Proposition 2B, the main operator is a:
a. Horseshoe.
b. Dot.
c. Tilde.
d. Wedge.
e. Triple bar.
INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
Statement 1B
(R • B) ≡ (B ⊃ ∼ R)
15. Statement 1B is:
a. Logically equivalent.
b. Tautologous.
c. Self-contradictory.
d. Contingent.
e. Consistent.
16. The truth table for Statement 1B has how many lines?
a. Six.
b. Four.
c. Two.
d. Eight.
e. Nine.
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21. Given the pair of statements:
J ≡ ∼ M and (J • M) ∨ ∼(M ∨ J)
These statements are:
a. Valid.
b. Consistent.
c. Contradictory.
d. Logically equivalent.
e. Inconsistent.
22. Given the pair of statements:
D • ∼ R and R • ∼ D
These statements are:
a. Logically equivalent.
b. Consistent.
c. Contradictory.
d. Valid.
e. Inconsistent.
23. Given the argument:
K ⊃ (M ∨ ∼ H) / M ⊃ H / M ⊃ K // K ⊃ H
This argument is:
a. Invalid; fails in 1st line.
b. Invalid; fails in 2nd line.
c. Valid.
d. Invalid; fails in 4th line.
e. Invalid; fails in 3rd line.
24. Given the argument:
R ∨ I / ∼ S ∨ (R ⊃ I) // S ⊃ I
This argument is:
a. Valid.
b. Invalid; fails in 4th line.
c. Invalid; fails in 2nd line.
d. Invalid; fails in 5th line.
e. Invalid; fails in 3rd line.
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INSTRUCTIONS: Use indirect truth tables to answer the following problems.
25. Given the argument:
Q ∨ ∼ S / ∼(N • A) / S ∨ A / (P • N) ∨ (G • Q) // P • G
This argument is:
a. Valid.
b. Uncogent.
c. Invalid.
d. Cogent.
e. Sound.
26. Given the argument:
J ⊃ C / R ∨ I / I ⊃ (U • ∼ J) / (R ∨ U) ⊃ (C • J) // C
This argument is:
a. Sound.
b. Uncogent.
c. Invalid.
d. Cogent.
e. Valid.
27. Given the statements:
Q ⊃ (N ∨ S) / N ⊃ (L ⊃ B) / (S ∨ E) ⊃ (Q ⊃ B) / Q ≡ ∼ B
These statements are:
a. Inconsistent.
b. Consistent.
c. Invalid.
d. Tautologous.
e. Logically equivalent.
28. Given the statements:
P ⊃ (A ⊃ M) / (D ∨ K) ⊃ (M ⊃ H) / (A • ∼ H) ∨ ∼ D / P • D
These statements are:
a. Contradictory.
b. Tautologous.
c. Valid.
d. Inconsistent.
INSTRUCTIONS: Determine whether the following symbolized arguments are valid or invalid by identifying the form
of each. In some cases the argument must be rewritten using double negation or commutativity before it has a named
form. Those arguments without a specific name are invalid.
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29. ∼D ⊃ ∼C
R ⊃ ∼D
R ⊃ ∼C
a. MP—valid.
b. DS—valid.
c. Invalid.
d. CD—valid.
e. HS—valid.
30. (∼C ⊃ ∼J) • (P ⊃ L)
J ∨ ∼L
C ∨ ∼P
a. CD—valid.
b. Invalid.
c. DD—valid.
d. MT—valid.
e. CD—invalid.
31. ∼M
M ⊃ ∼G
G
a. AC—invalid.
b. MT—valid.
c. DS—invalid.
d. DA—invalid.
e. MP—valid.
32. ∼N ∨ A
N
A
a. DS—valid.
b. HS—valid.
c. MT—valid.
d. DA—invalid.
e. MP—valid.
33. D ∨ ∼E
∼E
D
a. AC—invalid.
b. DS—invalid.
c. Invalid.
d. MP—valid.
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e. HS—valid.
34. ∼K ⊃ ∼N
∼K
∼N
a. HS—valid.
b. MP—valid.
c. MT—valid.
d. DS—valid.
e. AC—invalid.
35. ∼Q
H ⊃ ∼Q
H
a. MT—invalid.
b. MP—valid.
c. DA—invalid.
d. DS—valid.
e. AC—invalid.
36. E ⊃ ∼A
B ⊃ ∼E
B ⊃ A
a. Invalid.
b. DD—invalid.
c. HS—valid.
d. CD—valid.
e. DS—valid.
37. (∼H ⊃ K) • (H ⊃ ∼T)
H ∨ ∼H
∼T ∨ K
a. Invalid.
b. CD—valid.
c. DD—valid.
d. DA—invalid.
e. MP—valid.
38. ∼S ⊃ ∼F
F
S
a. MP—valid.
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b. DS—invalid.
c. DA—invalid.
d. MT—valid.
e. DS—valid.