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Chapter 06 Test I
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INSTRUCTIONS: Select the correct translation for each statement.
1. Hertz runs a sale or both Avis buys new cars and Budget lowers rates.
a. H ∨ A • B
b. H ∨ (A • B)
c. (H ∨ A) • B
d. H • (A ∨ B)
e. H • A ∨ B
2. Thrifty lays off workers only if neither National improves efficiency nor Enterprise reorganizes.
a. T ⊃ ∼(N ∨ E)
b. ∼(N ∨ E) ⊃ T
c. T ⊃ (∼N ∨ ∼T)
d. (∼N ∨ ∼E) ⊃ T
e. T ≡ ∼(N ∨ E)
3. Budget lowers rates unless Hertz and Thrifty do not overhaul operations.
a. B ∨ (∼H • ∼T)
b. B ∨ ∼(H • T)
c. B ⊃ (∼H • ∼T)
d. (∼H • ∼T) ⊃ B
e. (B ∨ ∼H) • ∼T
4. If National’s improving efficiency implies that Enterprise reorganizes, then Avis buys new cars.
a. (N ⊃ E ⊃ A)
b. N ⊃ (E ⊃ A)
c. (N ⊃ E) ⊃ A
d. A ⊃ (N ⊃ E)
e. (E ⊃ N) ⊃ A
5. Not both Hertz runs a sale and Thrifty lays off workers if either Avis buys new cars or Budget lowers rates.
a. (∼H • ∼T) ⊃ (A ∨ B)
b. (A ∨ B) ⊃ (∼H • ∼T)
c. ∼(H • T) ⊃ (A ∨ B)
d. (A ∨ B) ⊃ ∼(H • T)
e. (A • B) ⊃ ∼(H ∨ T)
6. National does not improve efficiency or Enterprise does not reorganize, given that Thrifty lays off workers.
a. T ⊃ ∼(N ∨ E)
b. (∼N ∨ ∼E) ⊃ T
c. ∼(N ∨ E) ⊃ T
d. (T ⊃ ∼N) ∨ ∼E
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e. T ⊃ (∼N ∨ ∼E)
7. Budget’s lowering rates implies that Hertz runs a sale, only if Avis does not buy new cars.
a. (B ⊃ H) ⊃ ∼A
b. ∼A ⊃ (B ⊃ H)
c. (B ⊃ H) ≡ ∼A
d. (H ⊃ B) ⊃ ∼A
e. (B ⊃ H ⊃ A)
8. Thrifty’s laying off workers is a sufficient condition for National’s improving efficiency, if Enterprise reorganizes.
a. E ⊃ (N ⊃ T)
b. (T ⊃ N) ⊃ E
c. E ⊃ (T ⊃ N)
d. T ⊃ (N ⊃ E)
e. E ≡ (T ⊃ N)
9. Hertz’s running a sale and Budget’s lowering rates are a necessary condition for either Avis’s buying new cars or
Thrifty’s laying off workers.
a. (A • T) ⊃ (H ∨ B)
b. (H • B) ⊃ (A ∨ T)
c. (H • B) ∨ (A ∨ T)
d. (A ∨ T) ⊃ (H • B)
e. (H • B) ≡ (A ∨ T)
10. National’s improving efficiency or Enterprise’s reorganizing is a sufficient and necessary condition for Thrifty’s laying
off workers, provided that Avis buys new cars.
a. (N ∨ E) ≡ (A ⊃ T)
b. A ⊃ [(N ∨ E) ≡ T]
c. [(N ∨ E) ≡ T] ⊃ A
d. A ⊃ [(N ⊃ E) • (E ⊃ N)]
e. A ≡ [(N ∨ E) ⊃ T]
Proposition 1I
Given the following proposition:
[(B ≡ ∼ Y) • ∼(∼ X ⊃ A)] ∨ [∼(X ≡ A) ⊃ (Y • ∼ A)]
11. Given that A and B are true and X and Y are false, determine the truth value of Proposition 1I.
a. True.
b. False.
12. In Proposition 1I, the main operator is a:
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Chapter 06 Test I
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a. Dot.
b. Tilde.
c. Horseshoe.
d. Triple bar.
e. Wedge.
Proposition 2I
Given the following proposition:
[∼(X ∨ B) ≡ (∼ Y ⊃ ∼ X)] ≡ ∼[(A ⊃ ∼ Y) • ∼(∼ X ⊃ ∼ B)]
13. Given that A and B are true and X and Y are false, determine the truth value of Proposition 2I.
a. True.
b. False.
14. In Proposition 2I, the main operator is a:
a. Tilde.
b. Wedge.
c. Horseshoe.
d. Triple bar.
e. Dot.
INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
Statement 1I
Given the following statement:
(G • ∼ M) ⊃ (M ∨ G)
15. Statement 1I is:
a. Consistent.
b. Logically equivalent.
c. Tautologous.
d. Contingent.
e. Self-contradictory.
16. The truth table for Statement 1I has how many lines?
a. Two.
b. Eight.
c. Four.
d. Six.
e. Nine.
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Chapter 06 Test I
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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 2I
Given the following statement:
(L • ∼ E) ≡ (E • ∼ L)
17. Statement 2I is:
a. Self-contradictory.
b. Tautologous.
c. Consistent.
d. Contingent.
e. Inconsistent.
INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
Statement 3I
Given the following statement:
[K • (P ∨ ∼ R)] • [K ⊃ (R • ∼ P)]
18. Statement 3I is:
a. Valid.
b. Self-contradictory.
c. Tautologous.
d. Inconsistent.
e. Contingent.
19. The truth table for Statement 3I has how many lines?
a. Six.
b. Nine.
c. Eleven.
d. Eight.
e. Four.
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 ∨ S and S ⊃ ∼ R
These statements are:
a. Inconsistent.
b. Contradictory.
c. Invalid.
d. Logically equivalent.
e. Consistent.
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21. Given the pair of statements:
(H • J) ∨ (N • J) and (N ∨ H) ⊃ ∼ J
These statements are:
a. Contradictory.
b. Valid.
c. Logically equivalent.
d. Consistent.
e. Inconsistent.
22. Given the argument:
K ∨ B / K ≡ (D ∨ ∼ B) // K ⊃ D
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.
23. Given the argument:
S ⊃ E / N ⊃ (∼ S ⊃ E) // N ⊃ E
This argument is:
a. Invalid; fails in 5th line.
b. Invalid; fails in 6th line.
c. Valid.
d. Invalid; fails in 2nd line.
e. Invalid; fails in 3rd line.
24. Given the argument:
G ⊃ (N • E) / H ⊃ N / K ⊃ ∼E / (H • K) ≡ G
This argument is:
a. Valid.
b. Invalid.
c. Uncogent.
d. Cogent.
e. Sound.
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25. Given the argument:
J ⊃ (E • Q) / ∼ Q ⊃ L / (E ∨ M) ⊃ (L ∨ ∼ Q) / M ∨ J // L
This argument is:
a. Valid.
b. Invalid.
c. Sound.
d. Cogent.
e. Uncogent.
26. Given the statements:
W ⊃ (E ∨ ∼ G) / A ⊃ (G ∨ ∼ E) / H ⊃ (A • W) / H • E
These statements are:
a. Inconsistent.
b. Tautologous.
c. Invalid.
d. Logically equivalent.
e. Consistent.
27. Given the statements:
∼ S ⊃ D / K ⊃ S / D ⊃ K / R ≡ ∼(S • C) / R ≡ C
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. ∼Q ∨ S
∼Q
S
a. Disjunctive syllogism.
b. Modus ponens.
c. Invalid.
d. Modus tollens.
e. Denying the antecedent.
29. (M ⊃ ∼T) • (∼H ⊃ T)
T ∨ ∼T
∼M ∨ H
a. Invalid.
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b. Destructive dilemma.
c. Constructive dilemma
d. Modus tollens.
e. Affirming the consequent.
30. K
G ⊃ ∼K
∼G
a. Disjunctive syllogism.
b. Invalid.
c. Denying the antecedent.
d. Modus tollens.
e. Affirming the consequent.
31. ∼G ∨ ∼B
B
∼G
a. Disjunctive syllogism.
b. Invalid.
c. Denying the antecedent.
d. Affirming the consequent.
e. Modus tollens.
32. F ⊃ ∼H
H ⊃ ∼T
F ⊃ T
a. Pure hypothetical syllogism.
b. Constructive dilemma.
c. Invalid.
d. Affirming the consequent.
e. Disjunctive syllogism.
33. R
R ⊃ ∼D
∼D
a. Invalid.
b. Affirming the consequent.
c. Disjunctive syllogism.
d. Modus tollens.
e. Modus ponens.
34. S ⊃ ∼C
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∼C
S
a. Modus tollens.
b. Affirming the consequent.
c. Denying the antecedent.
d. Modus ponens.
e. Invalid.
35. (∼W ⊃ L) • (N ⊃ ∼R)
N ∨ ∼W
L ∨ ∼R
a. Invalid.
b. Pure hypothetical syllogism.
c. Destructive dilemma.
d. Denying the antecedent.
e. Constructive dilemma.
36. E ⊃ ∼T
∼N ⊃ E
∼N ⊃ ∼T
a. Modus ponens.
b. Constructive dilemma.
c. Pure hypothetical syllogism.
d. Invalid.
e. Disjunctive syllogism.
37. ∼F ⊃ L
F
∼L
a. Denying the antecedent.
b. Modus ponens.
c. Affirming the consequent.
d. Modus tollens.
e. Invalid.
INSTRUCTIONS: Select the best answer for the following problems.
38. In the expression ‘P • Q’, ‘P’ is called:
a. A conjunction.
b. A disjunct.
c. An antecedent.
d. A conjunct.
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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 a group of statements are consistent, this means:
a. At least one of them is true.
b. It is possible for all of them to be true.
c. At least one of them is false.
d. All of them are true.
e. It is possible for all of them to be false.
41. If an indirect truth table requiring more than one line is constructed for either an argument or a series of statements
and a contradiction is derived on the first line, then:
a. The second line must be completed.
b. The argument is valid and the statements are consistent.
c. The argument is valid and the statements are inconsistent.
d. The argument is invalid and the statements are consistent.
e. The argument is invalid and the statements are inconsistent.
42. The wedge operator is used to translate:
a. “Nevertheless.”
b. “Moreover.”
c. “Unless.”
d. “Implies.”
e. “Provided that.”