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INSTRUCTIONS: Select the correct translation for each problem. Except for the truth table questions (which are double
credit), each question is worth 2 points.
1. Either Breitling has a diamond model and Rado advertises a calendar watch or Tissot has luminous hands.
a. B ∨ (R • T)
b. (B ∨ R) • T
c. (B • R) ∨ T
d. B • R ∨ T
e. B • (R ∨ T)
2. If Movado offers a blue dial, then neither Fossil is water resistant nor Nautica promotes a titanium case.
a. M ⊃ (∼F ∨ ∼N)
b. M ≡ ∼(F ∨ N)
c. M ⊃ (∼F • ∼N)
d. M ⊃ ∼(F ∨ N)
e. M ⊃ ∼F • ∼N
3. Piaget has a gold watch only if both Seiko has leather bands and Breitling has a diamond model.
a. P ⊃ (S • B)
b. (S • B) ∨ P
c. (S • B) ⊃ P
d. (S • B) ≡ P
e. S • (B ⊃ P)
4. Gucci features stainless steel; also, Fossil is water resistant given that Cartier offers a stop watch.
a. G ∨ (C ⊃ F)
b. (G • C) ⊃ F
c. G • (F ⊃ C)
d. C ⊃ (G • F)
e. G • (C ⊃ F)
5. Movado and Nautica offer a black dial if and only if Piaget has a gold watch.
a. (M ∨ N) ≡ P
b. (M • N) ≡ P
c. (M • N) ⊃ P
d. P ⊃ (N • N)
e. (P ⊃ M) • (P ⊃ N)
6. If Tissot has luminous hands, then if either Rado advertises a calendar model or Fossil is water resistant, then Gucci
features stainless steel.
a. (R ∨ F) ⊃ (T ⊃ G)
b. (R ⊃ T) ⊃ (F ⊃ G)
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c. [T ⊃ (R ∨ F)] ⊃ G
d. T ⊃ [(R ⊃ G) ∨ (F ⊃ G)]
e. T ⊃ [(R ∨ F) ⊃ G]
7. Cartier’s offering a stop watch implies that Seiko has leather bands, provided that both Rado advertises a calendar
model and Tissot has luminous hands.
a. (R • T) ⊃ (C ⊃ S)
b. (R ⊃ C) • (T ⊃ S)
c. (C ⊃ S) ⊃ (R • T)
d. [R ⊃ (C ⊃ S)] • [T ⊃ (C ⊃ S)]
e. (R ∨ T) ⊃ (C ⊃ S)
8. Movado’s offering an ivory dial is a sufficient condition for Breitling’s having a ruby model if Gucci’s offering a better
warranty is a necessary condition for Fossil’s being water resistant.
a. (M ⊃ B) ⊃ (F ⊃ G)
b. (B ⊃ M) ⊃ (G ⊃ F)
c. (G ⊃ F) ⊃ (B ⊃ M)
d. (F ⊃ G) ⊃ (M ⊃ B)
e. F ⊃ [G ⊃ (M ⊃ B)]
9. Piaget and Nautica do not have a sapphire watch unless Breitling’s having a diamond watch is a sufficient and necessary
condition for either Cartier’s offering multiple dials or Gucci’s selling a self-winder.
a. ∼(P • N) ∨ [(C ∨ G) ≡ B]
b. (∼P • ∼N) ∨ [(B ⊃ C) • (G ⊃ B)]
c. (∼P • ∼N) ∨ [(B ≡ (C ∨ G)]
d. (∼P • ∼N) ⊃ [(B ≡ (C ∨ G)]
e. [(B ≡ (C ∨G)] ⊃ (∼P • ∼N)
10. Seiko has a quartz watch if and only if either Movado does not offer a silver dial or Rado does not have a calendar
watch; however, Tissot has luminous hands only if both Fossil is water resistant and Rado has a calendar model.
a. [S ≡ ∼(M ∨ R)] • [T ⊃ (F • R)]
b. [S ≡ (∼M ∨ ∼R)] • [(F • R) ⊃ T]
c. [(∼M ∨ ∼R) ⊃ S] • [T ⊃ (F • R)]
d. [S ≡ (∼M ∨ ∼R)] ∨ [T ⊃ (F • R)]
e. [S ≡ (∼M ∨ ∼R)] • [T ⊃ (F • R)]
Proposition 1A
Given the following proposition:
[A ⊃ ∼ (B • Y)] ≡ ∼[B ⊃ (X • ∼ A)]
11. Given that A and B are true and X and Y are false, determine the truth value of Proposition 1A.
a. True.
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b. False.
12. In Proposition 1A, the main operator is a:
a. Tilde.
b. Wedge.
c. Triple bar.
d. Dot.
Proposition 2A
Given the following proposition:
[(X ⊃ A) • (B ⊃ ∼ Y)] ⊃ [(B ∨ Y) • (A ⊃ X)]
13. Given that A and B are true and X and Y are false, determine the truth value of Proposition 2A.
a. True.
b. False.
14. In Proposition 2A, the main operator is a:
a. Wedge.
b. Tilde.
c. Dot.
d. Horseshoe.
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 1A
Given the following statement:
(N ⊃ K) ≡ (K ⊃ N)
15. Statement 1A is:
a. Contingent.
b. Inconsistent.
c. Consistent.
d. Tautologous.
e. Self-contradictory.
16. The truth table for Statement 1A has how many lines?
a. Six.
b. Four.
c. Two.
d. Eight.
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e. Nine.
INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
Statement 2A
Given the following statement:
(G ⊃ ∼ Q) ≡ ∼(Q • G)
17. Statement 2A is:
a. Consistent.
b. Self-contradictory.
c. Tautologous.
d. Contingent.
e. Logically equivalent.
INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
Statement 3A
Given the following statement:
[∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)]
18. Statement 3A is:
a. Tautologous.
b. Valid.
c. Contingent.
d. Inconsistent.
e. Self-contradictory.
19. The truth table for Statement 3A has how many lines?
a. Four.
b. Eight.
c. Twelve.
d. Six.
e. Nine.
INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
20. Given the pair of statements:
∼ (R ≡ M) and M • ∼ R
These statements are:
a. Inconsistent.
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b. Invalid.
c. Logically equivalent.
d. Consistent.
e. Contradictory.
21. Given the pair of statements:
∼ (S ⊃ Q) and ∼ Q • S
These statements are:
a. Logically equivalent.
b. Valid.
c. Contradictory.
d. Consistent.
e. Inconsistent.
22. Given the pair of statements:
C • ∼ L and L • ∼ C
These statements are:
a. Consistent.
b. Inconsistent.
c. Contradictory.
d. Logically equivalent.
e. Valid.
23. Given the argument:
B ∨ M / B ∨ ∼ K // (K ∨ ∼ M) ⊃ B
This argument is:
a. Invalid; fails in 3rd line.
b. Invalid; fails in 2nd line.
c. Invalid; fails in 1st line.
d. Invalid; fails in 4th line.
e. Valid.
24. Given the argument:
S ≡ (N ∨ H) / S ∨ ∼N // S ⊃ H
This argument is:
a. Invalid; fails in 4th line.
b. Invalid; fails in 2nd line.
c. Invalid; fails in 5th line.
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d. Valid.
INSTRUCTIONS: Use indirect truth tables to answer the following problems.
25. Given the argument:
E ⊃ J / B ⊃ Q / D ⊃ (J • ∼ Q) // (E • B) ≡ D
This argument is:
a. Uncogent.
b. Sound.
c. Valid.
d. Invalid.
e. Cogent.
26. Given the argument:
(K • ∼ C) ⊃ ∼(P • R) / J ⊃ (K • P) / A ⊃ (P • R) // (A • J) ⊃ C
This argument is:
a. Cogent.
b. Sound.
c. Valid.
d. Uncogent.
e. Invalid.
27. Given the statements:
S ⊃ (Q ∨ L) / (Q ∨ G) ⊃ (S ⊃ N) / L ⊃ (N ∨ ∼ S) / S • ∼ N
These statements are:
a. Inconsistent.
b. Invalid.
c. Tautologous.
d. Logically equivalent.
e. Consistent.
28. Given the statements:
R ⊃ (M ∨ ∼ C) / (P ∨ U) ⊃ C / M ⊃ ∼ P / R ≡ U
These statements are:
a. Contradictory.
b. Tautologous.
c. Valid.
d. Inconsistent.
e. Consistent.
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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.
29. H ⊃ ∼M
M
∼H
a. DA—invalid.
b. MP—valid.
c. AC—invalid.
d. MT—valid.
e. HS—valid.
30. (∼G ∨ E) • (R ∨ M)
R ∨ ∼G
E ∨ M
a. MT—valid.
b. Invalid.
c. DA—invalid.
d. MP—valid.
e. AC—invalid.
31. (R ⊃ ∼T) • (D ⊃ T)
∼T ∨ T
∼R ∨ ∼D
a. MT—valid.
b. CD—invalid.
c. CD—valid.
d. HS—valid.
e. DD—valid.
32. ∼D ⊃ N
D
∼N
a. MP—valid.
b. MT—invalid.
c. DA—invalid.
d. AC—invalid.
e. Invalid.
33. ∼S
∼S ⊃ F
F
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a. MP—valid.
b. AC—valid.
c. MT—valid.
d. AC—invalid.
e. DS—valid.
34. S ∨ ∼T
S
∼T
a. DA—invalid.
b. CD—valid.
c. Invalid.
d. DD—valid.
e. CD—invalid.
35. ∼J ⊃ C
C ⊃ ∼T
∼J ⊃ ∼T
a. DD—valid.
b. MP—valid.
c. CD—valid.
d. Invalid.
e. HS—valid.
36. L
∼N ⊃ L
∼N
a. AC—invalid.
b. DA—invalid.
c. MP—valid.
d. MT—valid.
e. DS—invalid.
37. G ∨ ∼T
(G ⊃ ∼H) • (∼T ⊃ A)
∼H ∨ A
a. MP—valid.
b. CD—valid.
c. DD—valid.
d. Invalid.
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38. K ∨ ∼B
B
K
a. DA—invalid.
b. Invalid.
c. MT—valid.
d. DS—valid.
e. MP—valid.