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INSTRUCTIONS: Select the correct translation for each statement.
1. Delta advertises a sale and either United lowers fares or American hires pilots.
a. D • (U ∨ A)
b. D ∨ (U • A)
c. D • U ∨ A
d. (D • U) ∨ A
e. D ∨ (U • A)
2. Frontier’s improving service implies that not both JetBlue buys planes and Southwest expands routes.
a. F ⊃ ∼(J ∨ S)
b. F ⊃ (∼J • ∼S)
c. F ⊃ ∼(J • S)
d. (F ⊃ ∼J) • S
e. F ≡ ∼(J • S)
3. JetBlue buys planes unless neither Frontier improves service nor United lowers fares.
a. J ∨ ∼(F • U)
b. J ∨ ∼(F ∨ U)
c. J ∨ (∼F ∨ ∼U)
d. J ⊃ ∼(F ∨ U)
e. ∼(F ∨ U) ⊃ J
4. American’s hiring pilots is a sufficient condition for both Delta’s advertising a sale and Southwest’s expanding routes.
a. (D • S) ∨ A
b. (D ⊃ A) • (S ⊃ A)
c. (D • S) ⊃ A
d. A ⊃ (D • S)
e. A ≡ (D • S)
5. Frontier’s improving service is a necessary condition for either JetBlue’s buying planes or United’s lowering fares.
a. F ≡ (J ∨ U)
b. F ⊃ (J ∨ U)
c. (F ⊃ J) • (F ⊃ U)
d. (J ∨ U) ⊃ F
e. (J ⊃F) ∨ (F ⊃ U)
6. Southwest expands routes if either American does not hire pilots or United does not lower fares.
a. ∼(A ∨ U) ⊃ S
b. (∼A • ∼U) ⊃ S
c. S ⊃ (∼A ∨ ∼U)
d. (S ⊃ ∼A ∨ ∼U)
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e. (∼A ∨ ∼U) ⊃ S
7. JetBlue buys planes if and only if both Delta does not advertise a sale and Southwest does not expand routes.
a. J ≡ ∼(D • S)
b. J ⊃ (∼D • ∼S)
c. J ≡ (∼D • ∼S)
d. ∼(D ∨ S) ⊃ J
e. J ∨ (∼D • ∼S)
8. United’s lowering fares is a sufficient and necessary condition for American’s hiring pilots, given that Frontier does not
improve service.
a. (U ≡ A) ⊃ ∼F
b. ∼F ⊃ (U ≡ A)
c. (∼F ⊃ U) • (∼F ⊃ A)
d. (∼F ≡ U) • (∼F ≡ A)
e. ∼F ≡ (U ⊃ A)
9. JetBlue buys planes if Delta advertises a sale, and Frontier improves service only if Southwest expands routes.
a. (D ⊃ J) • (F ⊃ S)
b. (D ≡ J) • (F ≡ S)
c. (J ⊃ D) • (S ⊃ F)
d. (D • J) ⊃ (S • F)
e. (J ⊃ D) • (F ⊃ S)
10. United lowers fares if and only if both JetBlue buys planes and Delta advertises a sale, provided that American hires
pilots.
a. (U ≡ A) • (J ≡ D)
b. A ⊃ [U ≡ (J • D)]
c. [U ≡ (J • D)] ⊃ A
d. A ⊃ [(U ⊃ J) • (D ⊃ U]
e. [U ⊃ (J • D)] ⊃ A
Proposition 1H
Given the following proposition:
[(A ≡ ∼B) ∨ (X ⊃ Y)] • [(Y ⊃ A) ≡ ∼(X ∨ B)]
11. Given that A and B are true and X and Y are false, determine the truth value of Proposition 1H.
a. True.
b. False.
12. In Proposition 1H, the main operator is a:
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a. Horseshoe.
b. Tilde.
c. Dot.
d. Triple bar.
e. Wedge.
Proposition 2H
Given the following proposition:
∼[(B • ∼X) ⊃ ∼(Y ≡ ∼B)] ⊃ [∼(X ⊃ A) ∨ (B ⊃ ∼Y)]
13. Given that A and B are true and X and Y are false, determine the truth value of Proposition 2H.
a. True.
b. False.
14. In Proposition 2H, the main operator is a:
a. Dot.
b. Wedge.
c. Triple bar.
d. Tilde.
INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
Statement 1H
Given the following statement:
(S ⊃ ∼ R) ⊃ (∼ S • R)
15. Statement 1H is:
a. Consistent.
b. Logically equivalent.
c. Tautologous.
d. Contingent.
e. Self-contradictory.
16. The truth table for Statement 1H has how many lines?
a. Two.
b. Eight.
c. Four.
d. Six.
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 2H
Given the following statement:
[N ∨ ∼ (K ∨ G)] ≡ [(G ⊃ N) • (K ⊃ N)]
17. Statement 2H is:
a. Inconsistent.
b. Contingent.
c. Consistent.
d. Self-contradictory.
e. Tautologous.
18. The truth table for Statement 2H has how many lines?
a. Five.
b. Nine.
c. Eight.
d. Six.
INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
19. Given the statement:
(E ∨ ∼ H) • (H • ∼ E)
This statement is:
a. Valid.
b. Self-contradictory.
c. Tautologous.
d. Inconsistent.
e. Contingent.
20. Given the pair of statements:
G ⊃ (W • ∼ Q) and (W ∨ ∼ G) • ∼(Q • G)
These statements are:
a. Inconsistent.
b. Contradictory.
c. Invalid.
d. Logically equivalent.
e. Consistent.
21. Given the pair of statements:
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P • ∼ Z and Z ≡ P
These statements are:
a. Inconsistent.
b. Valid.
c. Contradictory.
d. Consistent.
e. Logically equivalent.
22. Given the argument:
M ⊃ J / ∼ J ⊃ R // (M ∨ ∼ R) ⊃ J
This argument is:
a. Invalid; fails in 3rd line.
b. Invalid; fails in 2nd line.
c. Invalid; fails in 4th line.
d. Invalid; fails in 1st line.
e. Valid.
23. Given the argument:
Q ⊃ A / ∼ (A • Q) / A ≡ Q
This argument is:
a. Invalid; fails in 1st line.
b. Valid.
c. Invalid; fails in 3rd line.
d. Invalid; fails in 2nd line.
e. Invalid; fails in 4th line.
INSTRUCTIONS: Use indirect truth tables to answer the following problems.
24. Given the argument:
R ⊃ (H • ∼N) / (H • ∼B) ⊃ (N ∨ ∼P) / K ⊃ (G • P) // (K • R) ⊃ B
This argument is:
a. Invalid.
b. Valid.
c. Uncogent.
d. Cogent.
e. Sound.
25. Given the argument:
S ⊃ W / C ⊃ L / (M • ∼L) ∨ (D • ∼W) / C ∨ S // D • M
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This argument is:
a. Invalid.
b. Cogent.
c. Sound.
d. Valid.
e. Uncogent.
26. Given the statements:
H ⊃ E / M ⊃ R / (M • E) ⊃ G / (R • G) ⊃ E / M ∨ E
These statements are:
a. Invalid.
b. Tautologous.
c. Consistent.
d. Logically equivalent.
e. Inconsistent.
27. Given the statements:
C ⊃ L / K ⊃ ∼H / L ⊃ (N ⊃ K) / C ⊃ (H ⊃ N) / C • H
These statements are:
a. Contradictory.
b. Tautologous.
c. Consistent.
d. Inconsistent.
e. Valid.
INSTRUCTIONS: Identify the form of each argument. Those without a specific name are invalid.
28. B ⊃ ∼Q
Q
∼B
a. Modus ponens.
b. Modus tollens.
c. Disjunctive syllogism.
d. Invalid.
e. Denying the antecedent.
29. (∼N ⊃ R) • (F ⊃ ∼G)
F ∨ ∼N
R ∨ ∼G
a. Constructive dilemma.
b. Invalid.
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c. Denying the antecedent.
d. Modus tollens.
e. Destructive dilemma.
30. ∼H ⊃ ∼B
K ⊃ ∼H
K ⊃ ∼B
a. Denying the antecedent.
b. Invalid.
c. Pure hypothetical syllogism.
d. Constructive dilemma.
e. Destructive dilemma.
31. D ⊃ ∼N
∼N
D
a. Affirming the consequent.
b. Invalid.
c. Denying the antecedent.
d. Modus ponens.
e. Modus tollens.
32. S ⊃ ∼R
N ⊃ ∼R
S ⊃ N
a. Disjunctive syllogism.
b. Constructive dilemma.
c. Pure hypothetical syllogism.
d. Affirming the consequent.
e. Invalid.
33. ∼P ∨ M
P
M
a. Modus tollens.
b. Denying the antecedent.
c. Pure hypothetical syllogism.
d. Disjunctive syllogism.
e. Invalid.
34. ∼L ⊃ F
L
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∼F
a. Disjunctive syllogism.
b. Denying the antecedent.
c. Modus tollens.
d. Modus ponens.
e. Invalid.
35. ∼G
∼G ⊃ A
A
a. Constructive dilemma.
b. Disjunctive syllogism.
c. Modus ponens.
d. Denying the antecedent.
e. Invalid.
36. G ∨ ∼T
∼T
G
a. Invalid.
b. Disjunctive syllogism.
c. Modus ponens.
d. Affirming the consequent.
e. Modus tollens.
37. (K ⊃ ∼A) • (S ⊃ ∼D)
A ∨ D
∼K ∨ ∼S
a. Invalid.
b. Modus tollens.
c. Affirming the consequent.
d. Denying the antecedent.
INSTRUCTIONS: Select the best answer for the following problems.
38. In the expression ‘P ∨ Q’, ‘P’ is called:
a. A disjunction.
b. A conjunct.
c. A disjunct.
d. A conjunction.
e. An antecedent.
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39. According to De Morgan’s rule, ∼(P ∨ Q) is logically equivalent to:
a. P ∨ Q
b. ∼P ∨ ∼Q
c. P • Q
d. ∼P • ∼Q
e. P ≡ Q
40. If an indirect truth table requiring more than one line is constructed for either an argument or a series of statements
and no contradiction is derived on the first line, then:
a. The argument is valid and the statements are consistent.
b. The argument is invalid and the statements are consistent.
c. The argument is valid and the statements are inconsistent.
d. The argument is invalid and the statements are inconsistent.
e. The second line of the truth table must be completed.
41. If a group of statements are inconsistent, this means:
a. It is not possible for all of them to be true.
b. All of them are false.
c. At least one of them is false.
d. It is possible for all of them to be false.
e. Exactly one of them is false.
42. The dot operator is used to translate:
a. “Either.”
b. “Unless.”
c. “Implies.”
d. “Provided that.”
e. “Moreover.”