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INSTRUCTIONS: Select the correct translation for each problem.
1. Amherst reduces class size, and either Williams increases enrollment or Smith raises tuition.
a. A • (W ⊃ S)
b. A • (W ∨ S)
c. (A • W) ∨ S
d. A ⊃ (W ∨ S)
e. A ∨ (W • S)
2. If Williams increases enrollment, then not both Fordham and Georgetown expand course offerings.
a. W ∨ ∼(F ⊃ G)
b. W ⊃ ∼(F ∨ G)
c. W ⊃ (∼F • ∼G)
d. W ≡ ∼(F • G)
e. W ⊃ ∼(F • G)
3. Rice hires new faculty only if neither Duke nor Tulane increases student aid.
a. ∼(D ∨ T) ⊃ R
b. R ≡ ∼(D ∨ T)
c. R ⊃ ∼(D ∨ T)
d. R ⊃ (∼D ∨ ∼T)
e. (∼D ∨ ∼T) ⊃ R
4. Both Baylor and Rice do not raise tuition provided that Smith increases enrollment.
a. S ⊃ (∼B • ∼R)
b. (∼B • ∼R) ∨ S
c. (∼B • ∼R) ⊃ S
d. S ⊃ ∼(B • R)
e. ∼(B • R) ⊃ S
5. Williams offers new scholarships if and only if either Amherst reduces class size or Smith does not hire new faculty.
a. (A ∨ S) ⊃ W
b. W ≡ ∼(A ∨ S)
c. W ⊃ (A ∨ ∼S)
d. W ≡ (A ∨ ∼S)
e. (W ≡ A) ∨ ∼S
6. If Fordham expands course offerings, then if Georgetown increases its endowment, then both Duke raises tuition and
Tulane reduces class size.
a. (F ⊃ G) ⊃ (D • T)
b. [F ⊃ (G ⊃ D)] • T
c. F ⊃ [G ⊃ (D • T)]
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d. F [(G ⊃ D) T]
e. F ⊃ G ⊃ (D • T)
7. If Baylor’s hiring new faculty implies that Rice increases enrollment, then Williams raises tuition if Smith expands
course offerings.
a. (R ⊃ B) ⊃ (S ⊃ W)
b. (B ⊃ R) ≡ (S ⊃ W)
c. S ⊃ [(B ⊃ R) ⊃ W]
d. B ⊃ [R ⊃ S ⊃ W)]
e. (B ⊃ R) ⊃ (S ⊃ W)
8. Tulane increasing enrollment is a necessary condition for Duke’s reducing class size if and only if Fordham’s raising
tuition is a sufficient condition for Georgetown’s expanding course offerings.
a. (D ∨ T) ≡ (F ∨ G)
b. (D ⊃ T) ≡ (F ⊃ G)
c. (T ⊃ D) ≡ (G ⊃ F)
d. (F ⊃ G) ⊃ (D ⊃ T)
e. (D ⊃ T) ⊃ (F ⊃ G)
9. Rice’s reducing class size is a sufficient and necessary condition for Baylor’s hiring new faculty unless Amherst’s
raising tuition implies that either Georgetown or Fordham does not offer new scholarships.
a. (R ≡ B) ∨ [A ⊃ (∼G ∨ ∼F)]
b. (B ⊃ R) ∨ [A ⊃ ∼(G • F)]
c. (R ⊃ B) ⊃ [A ⊃ (∼G ∨ ∼F)]
d. [A ⊃ (∼G ∨ ∼F)] ⊃ (R ≡ B)
e. (R ≡ B) ∨ [A ⊃ ∼(G ∨ F)]
10. Williams hires new faculty if either Smith increases enrollment or Amherst does not raise tuition, but Tulane reduces
class size only if neither Rice expands course offerings nor Baylor offers new scholarships.
a. [W ⊃ ∼(S ∨ A)] ∨ [T ⊃ ∼(R ∨ B)]
b. [T ⊃ ∼(R ∨ B)] ⊃ [(S ∨ ∼A) ⊃ W]
c. [W ⊃ (S ∨ ∼A)] • [∼(R ∨ B) ⊃ T]
d. [(S ∨ ∼A) ⊃ W] • [T ⊃ ∼(R ∨ B)]
e. [(S ∨ ∼A) ⊃ W] • [T ⊃ (∼R ∨ ∼B)]
Proposition 1D
Given the following proposition:
∼ (A • ∼ X) ≡ [A ⊃ (Y ∨ ∼ B)]
11. Given that A and B are true and X and Y are false, determine the truth value of Proposition 1D.
a. True.
b. False.
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12. In Proposition 1D, the main operator is a:
a. Tilde.
b. Wedge.
c. Horseshoe.
d. Dot.
e. Triple bar.
Proposition 2D
Given the following proposition:
[(A • ∼ X) ⊃ (∼ B ≡ Y)] • [∼ (Y ∨ ∼ A) ≡ (B • X)]
13. Given that A and B are true and X and Y are false, determine the truth value of Proposition 2D.
a. True.
b. False.
14. In Proposition 2D, the main operator is a:
a. Wedge.
b. Horseshoe.
c. Dot.
d. Tilde.
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 1D
Given the following statement:
∼ (H ⊃ A) ∨ (A ⊃ H)
15. Statement 1D is:
a. Self-contradictory.
b. Inconsistent.
c. Consistent.
d. Tautologous.
e. Contingent.
16. The truth table for Statement 1D has how many lines?
a. Six.
b. Eight.
c. Two.
d. Four.
e. Nine.
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INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
Statement 2D
Given the following statement:
[(N ∨ R) ⊃ ∼ R] ≡ R
17. Statement 2D 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 3D
Given the following statement:
(M ⊃ ∼ E) ∨ (R ⊃ E)
18. Statement 3D is:
a. Tautologous.
b. Self-contradictory.
c. Contingent.
d. Inconsistent.
e. Valid.
19. The truth table for Statement 3D has how many lines?
a. Four.
b. Nine.
c. Twelve.
d. Six.
e. Eight.
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:
M ⊃ L and ∼ (L ⊃ M)
These statements are:
a. Inconsistent.
b. Invalid.
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c. Consistent.
d. Logically equivalent.
e. Contradictory.
21. Given the pair of statements:
∼ (Q ⊃ ∼ A) and A • Q
These statements are:
a. Consistent.
b. Valid.
c. Contradictory.
d. Logically equivalent.
e. Inconsistent.
22. Given the pair of statements:
N ∨ (E • ∼ H) and (H • ∼ N) ∨ ∼ (E ∨ N)
These statements are:
a. Consistent.
b. Contradictory.
c. Inconsistent.
d. Logically equivalent.
e. Valid.
23. Given the argument:
S ⊃ (K ∨ ∼ S) / K ⊃ S // S ≡ K
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:
M ⊃ Q / M ∨ ∼ Q // M • Q
This argument is:
a. Invalid; fails in 4th line.
b. Valid.
c. Invalid; fails in 5th line.
d. Invalid; fails in 2nd line.
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e. Invalid; fails in 3rd line.
INSTRUCTIONS: Use indirect truth tables to answer the following problems.
25. Given the argument:
R ⊃ (G • D) / N ⊃ (A • L) / R ∨ N / L ⊃ K // D • K
This argument is:
a. Uncogent.
b. Sound.
c. Invalid.
d. Valid.
e. Cogent.
26. Given the argument:
(S ∨ B) ⊃ M / S ∨ ∼ Q / A ⊃ B / A ∨ Q // M
This argument is:
a. Cogent.
b. Valid.
c. Sound.
d. Uncogent.
e. Invalid.
27. Given the statements:
N ⊃ (L • S) / (S ∨ W) ⊃ B / G ⊃ ∼ B / G ⊃ N
These statements are:
a. Consistent.
b. Invalid.
c. Tautologous.
d. Logically equivalent.
e. Inconsistent.
28. Given the statements:
R ⊃ M / C ⊃ E / M ⊃ ∼ E / R • C
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. L
∼E ⊃ ∼L
E
a. DA—invalid.
b. MP—valid.
c. MT—valid.
d. AC—invalid.
e. HS—valid.
30. E ∨ ∼N
∼N
∼E
a. AC—invalid.
b. MT—valid.
c. DA—invalid.
d. MP—valid.
e. Invalid.
31. (∼H ⊃ B) • (L ⊃ ∼T)
T ∨ ∼B
H ∨ ∼L
a. MT—valid.
b. DD—valid.
c. CD—valid.
d. HS—valid.
e. CD—invalid.
32. M
∼M ⊃ G
∼G
a. MP—valid.
b. MT—invalid.
c. AC—invalid
d. DA—invalid.
e. Invalid.
33. ∼T ⊃ ∼W
∼T
∼W
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a. MP—valid.
b. AC—valid.
c. MT—valid.
d. AC—invalid.
e. DS—valid.
34. (L ⊃ ∼C) • (D ⊃ ∼Q)
∼L ∨ ∼D
C ∨ Q
a. DA—invalid.
b. CD—valid.
c. Invalid.
d. DD—valid.
e. CD—invalid.
35. ∼A ⊃ ∼H
E ⊃ ∼A
E ⊃ ∼H
a. DD—valid.
b. MP—valid.
c. CD—valid.
d. Invalid.
e. HS—valid.
36. ∼P ⊃ ∼D
∼D
∼P
a. MP—valid.
b. DA—invalid.
c. AC—invalid.
d. MT—valid.
e. DS—invalid.
37. (S ⊃ Q) • (∼W ⊃ ∼C)
∼W ∨ S
Q ∨ ∼C
a. MP—valid.
b. Invalid.
c. DD—valid.
d. CD—valid.
e. DD—invalid.
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38. Q ∨ ∼S
S
Q
a. DA—invalid.
b. DS—valid.
c. MT—valid.
d. Invalid.
e. MP—valid.