Name:
Class:
Date:
Chapter 06 Test G
Copyright Cengage Learning. Powered by Cognero.
Page 1
INSTRUCTIONS: Select the correct translation for each statement.
1. Either Fiat improves mileage and Toyota closes a factory or Honda reduces inventory.
a. F • (T ∨ H)
b. F • T ∨ H
c. (F ∨ T) • H
d. (F • T) ∨ H
e. F ∨ T • H
2. If Chrysler increases sales, then it is not the case that both Mercedes introduces a new model and Nissan lays off
workers.
a. C ⊃ (∼M • ∼N)
b. (C ⊃ ∼M) • N
c. C ⊃ ∼(M • N)
d. C ⊃ ∼M • ∼N
e. ∼(M • N) ⊃ C
3. If Nissan lays off workers, then if Toyota closes a factory, then neither Honda nor Fiat reduces inventory.
a. N ⊃ [T ⊃ ∼(H ∨ F)]
b. N ⊃ T ⊃ ∼(H ∨ F)
c. (N ⊃ T) ⊃ ∼(H ∨ F)
d. (N ⊃ T) ⊃ (∼H ∨ ∼F)
e. N ⊃ [T ⊃ (∼H ∨ ∼F)]
4. Either Chrysler’s increasing sales is a necessary condition for Toyota’s closing a factory or Nissan’s laying off workers
is a sufficient condition for Honda’s reducing inventory.
a. T ⊃ [C ⊃ (N ⊃ H)]
b. (C ⊃ T) ∨ (N ⊃ H)
c. (T ⊃ C) ∨ (N ⊃ H)
d. T ⊃ [C ∨ (N ⊃ H)]
e. (C ⊃ T) ∨ (H ⊃ N)
5. Honda reduces inventory if and only if Mercedes does not introduce a new model, unless Toyota closes a factory.
a. (H ⊃ ∼M) ∨ (∼M ⊃ T)
b. (H ≡ ∼M) ∨ T
c. T ⊃ (H ≡ ∼M)
d. H ≡ (∼M ∨ T)
e. (H ⊃ ∼M) ∨ T
6. Chrysler increases sales only if Honda reduces inventory, provided that Nissan does not lay off workers.
a. (C ≡ H) ⊃ ∼N
b. (C ⊃ H) ⊃ ∼N
Name:
Class:
Date:
Chapter 06 Test G
Copyright Cengage Learning. Powered by Cognero.
Page 2
c. (H ⊃ C) ⊃ ∼N
d. ∼N ⊃ (H ⊃ C)
e. ∼N ⊃ (C ⊃ H)
7. Both Nissan lays off workers if Fiat improves mileage and Honda reduces inventory only if Mercedes introduces a new
model.
a. [F ⊃ (N • H)] ⊃ M
b. (F ⊃ N) • (H ⊃ M)
c. (N ≡ F) • (H ≡ M)
d. (N ⊃ F) • (M ⊃ H)
e. (F ⊃ N) ≡ (H ⊃ M)
8. Toyota’s closing a factory implies that Fiat improves mileage, given that both Chrysler and Nissan do not increase sales.
a. (∼C • ∼N) ⊃ (T ⊃ F)
b. (T ⊃ F) ⊃ (∼C • ∼N)
c. ∼(C • N) ⊃ (T ⊃ F)
d. T ⊃ [(∼C • ∼N) ⊃ F]
e. T ⊃ [F ⊃ (∼C • ∼N)]
9. It is not the case that either Honda reduces inventory and Mercedes introduces a new model or Toyota closes a factory
and Fiat improves mileage.
a. ∼(H • M) ∨ ∼(T • F)
b. (∼H • ∼M) ∨ (∼T • ∼F)
c. ∼[(H • M) ∨ (T • F)]
d. ∼(H ∨ M) • ∼(T ∨ F)
e. ∼ [(H ∨ M) • (T ∨ F)]
10. Honda’s reducing inventory is a sufficient and necessary condition for Toyota’s closing a factory; also, Nissan lays off
workers only if either Chrysler or Fiat does not improve mileage.
a. (H ⊃ T) • [N ⊃ ∼(C ∨ F)]
b. H ≡ {T ⊃ [N ⊃ (∼C ∨ ∼F)]}
c. [H ≡ (T • N)] ⊃ (∼C ∨ ∼F)
d. (H ≡ T) • [(∼C ∨ ∼F) ⊃ N]
e. (H ≡ T) • [N ⊃ (∼C ∨ ∼F)]
Proposition 1G
Given the following proposition:
[(A ≡ X) ∨ (Y ⊃ ∼ B)] ⊃ ∼[(X ∨ B) • (A • Y)]
11. Given that A and B are true and X and Y are false, determine the truth value of Proposition 1G.
a. True.
b. False.
Name:
Class:
Date:
Chapter 06 Test G
Copyright Cengage Learning. Powered by Cognero.
Page 3
12. In Proposition 1G, the main operator is a:
a. Dot.
b. Tilde.
c. Horseshoe.
d. Triple bar.
e. Wedge.
Proposition 2G
Given the following proposition:
∼[(A ⊃ Y) ∨ ∼(X ⊃ B)] • [∼(A ≡ ∼X) ∨ (B ⊃ X)]
13. Given that A and B are true and X and Y are false, determine the truth value of Proposition 2G.
a. True.
b. False.
14. In Proposition 2G, the main operator is a:
a. Triple bar.
b. Wedge.
c. Horseshoe.
d. Tilde.
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 1G
Given the following statement:
(A • B) ≡ (∼A • ∼B)
15. Statement 1G is:
a. Consistent.
b. Logically equivalent.
c. Tautologous.
d. Contingent.
e. Self-contradictory.
16. The truth table for Statement 1G has how many lines?
a. Four.
b. Eight.
c. Two.
d. Six.
e. Nine.
Name:
Class:
Date:
Chapter 06 Test G
Copyright Cengage Learning. Powered by Cognero.
Page 4
INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the
instructions in the textbook.
Statement 2G
Given the following statement:
∼ (B ∨ A) ≡ (∼ A ⊃ B)
17. Statement 2G is:
a. Tautologous.
b. Contingent.
c. Consistent.
d. Self-contradictory.
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 3G
Given the following statement:
[A • (B ∨ C)] ∨ [∼ (A • B) ∨ ∼ (A • C)]
18. Statement 3G is:
a. Valid.
b. Self-contradictory.
c. Tautologous.
d. Inconsistent.
e. Contingent.
19. The truth table for Statement 3G 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:
(A ∨ B) • (∼ A ∨ ∼ B) and (B • A) ∨ (∼ A • ∼ B).
These statements are:
a. Inconsistent.
b. Contradictory.
Name:
Class:
Date:
Chapter 06 Test G
Copyright Cengage Learning. Powered by Cognero.
Page 5
c. Invalid.
d. Logically equivalent.
e. Consistent.
21. Given the pair of statements:
A ∨ (B • C) and (B • ∼ A) ∨ (A • ∼ C).
These statements are:
a. Logically equivalent.
b. Valid.
c. Contradictory.
d. Consistent.
e. Inconsistent.
22. Given the argument:
A ⊃ ∼B / B ∨ A // ∼B ≡ A.
This argument is:
a. Invalid; fails in 4th line.
b. Invalid; fails in 2nd line.
c. Valid.
d. Invalid; fails in 1st line.
e. Invalid; fails in 3rd line.
23. Given the argument:
A ⊃ (B • ∼ C) / B ⊃ (C ∨ A) / C ⊃ ∼ A // C ⊃ ∼ B.
This argument is:
a. Invalid; fails in 6th line.
b. Valid.
c. Invalid; fails in 5th line.
d. Invalid; fails in 2nd line.
e. Invalid; fails in 3rd line.
INSTRUCTIONS: Use indirect truth tables to answer the following problems.
24. Given the argument:
(A • B) ∨ (C • D) / E ⊃ ∼ B / F ⊃ ∼ D / E ∨ F // A • C.
This argument is:
a. Valid.
b. Invalid.
c. Uncogent.
d. Cogent.
e. Sound.
Name:
Class:
Date:
Chapter 06 Test G
Copyright Cengage Learning. Powered by Cognero.
Page 6
25. Given the argument:
(A • B) ≡ (C ∨ D) / A ⊃ E / B ⊃ F // C ⊃ (E • F).
This argument is:
a. Cogent.
b. Invalid.
c. Sound.
d. Valid.
e. Uncogent.
26. Given the statements:
A ⊃ (B • C) / B ⊃ (D ∨ ∼ E) / C ⊃ (E ∨ ∼ D) / A • E.
These statements are:
a. Consistent.
b. Tautologous.
c. Invalid.
d. Logically equivalent.
e. Inconsistent.
27. Given the statements:
A ≡ (B ∨C) / B ⊃ D / D ⊃ E / E ⊃ ∼ B / A ≡ ∼ C.
These statements are:
a. Valid.
b. Tautologous.
c. Consistent.
d. Contradictory.
e. Inconsistent.
INSTRUCTIONS: Identify the form of each argument. Those without a specific name are invalid.
28. Either taxes will be imposed on sugary drinks or public health will deteriorate. Therefore, public health will
deteriorate, since taxes will not be imposed on sugary drinks.
a. Modus tollens.
b. Modus ponens.
c. Disjunctive syllogism.
d. Invalid.
e. Denying the antecedent.
29. If rainfall is normal, then grain reserves will not be tapped, because if the harvest is not abundant, then grain reserves
will be tapped, and if rainfall is normal, then the harvest will be abundant.
Name:
Class:
Date:
Chapter 06 Test G
Copyright Cengage Learning. Powered by Cognero.
Page 7
a. Pure hypothetical syllogism.
b. Invalid.
c. Denying the antecedent.
d. Modus tollens.
e. Affirming the consequent.
30. If our company reduces wages, then it will lose its labor force; but if it does not reduce wages, then it will go
bankrupt. Thus, our company will either lose its labor force or go bankrupt, since it will either reduce wages or not reduce
them.
a. Constructive dilemma.
b. Invalid.
c. Denying the antecedent.
d. Pure hypothetical syllogism.
e. Destructive dilemma.
31. If computers can play chess, then they can think. But computers cannot think. Thus, computers cannot play chess.
a. Disjunctive syllogism.
b. Invalid.
c. Denying the antecedent.
d. Affirming the consequent.
e. Modus tollens.
32. If the nuts are stale, then they should not be put into the salad. Thus, the nuts are stale, since they should not be put
into the salad.
a. Modus ponens.
b. Denying the antecedent.
c. Invalid.
d. Affirming the consequent.
e. Disjunctive syllogism.
33. If dinosaur DNA has deteriorated, then it is impossible to recreate dinosaurs. If dinosaurs perished long ago, then
dinosaur DNA has deteriorated. Hence, if dinosaurs perished long ago, then it is impossible to recreate them.
a. Constructive dilemma.
b. Affirming the consequent.
c. Pure hypothetical syllogism.
d. Modus tollens.
e. Invalid.
34. Either we recycle our trash or we will be inundated in garbage. Therefore, we will not be inundated in garbage, since
we recycle our trash.
a. Disjunctive syllogism.
b. Destructive dilemma.
c. Pure hypothetical syllogism.
Name:
Class:
Date:
Chapter 06 Test G
Copyright Cengage Learning. Powered by Cognero.
Page 8
d. Modus ponens.
e. Invalid.
35. If deficit spending is halted, then interest rates will drop; but if inflation heats up, then interest rates will not drop.
Accordingly, either deficit spending will not be halted or inflation will not heat up, since interest rates will either drop or
not drop.
a. Destructive dilemma.
b. Pure hypothetical syllogism.
c. Constructive dilemma.
d. Denying the antecedent.
e. Invalid.
36. French has many irregular verbs. But if that is so, then French is harder to learn than English. Thus, French is harder
to learn than English.
a. Denying the antecedent.
b. Constructive dilemma.
c. Modus ponens.
d. Affirming the consequent.
e. Modus tollens.
37. If eggs do not contain cholesterol, then they are healthy to eat. But eggs do contain cholesterol. Thus, eggs are not
healthy to eat.
a. Modus tollens.
b. Modus ponens.
c. Affirming the consequent.
d. Denying the antecedent.
e. Invalid.
INSTRUCTIONS: Select the best answer for the following problems.
38. Escaping between the horns of a dilemma means:
a. Proving the dilemma unsound by proving the conjunctive premise false.
b. Proving the dilemma unsound by proving it invalid.
c. Proving the dilemma invalid by proving the conjunctive premise false.
d. Proving the dilemma invalid by proving the disjunctive premise false.
e. Proving the dilemma unsound by proving the disjunctive premise false.
39. When the disjunctive premise of a dilemma is of the form p ∨ ∼p, then it is impossible to:
a. Grasp it by the horns.
b. Escape between the horns.
c. Construct a counterdilemma.
d. Prove it valid.
e. Prove it sound.
Name:
Class:
Date:
Chapter 06 Test G
Copyright Cengage Learning. Powered by Cognero.
Page 9
40. If an ordinary truth table is constructed for a valid argument, then:
a. There may be one line that has true premise(s) and false conclusion.
b. There is no line that has true premise(s) and false conclusion.
c. There must be at least one line that has true premise(s) and false conclusion.
d. There must be at least one line that has true premise(s) and true conclusion.
e. There must be exactly one line that has true premise(s) and true conclusion.
41. Suppose an indirect truth table is constructed for an argument, and the truth table requires more than one line. If no
contradiction is obtained on the first line, then:
a. The argument is valid.
b. The argument could still be valid.
c. The argument is invalid.
d. The argument is consistent.
e. The argument is sound.
42. Suppose an indirect truth table is constructed for a series of statements, and the truth table requires more than one line.
If a contradiction is reached on the first line, then:
a. The statements are consistent.
b. The statements are contingent.
c. The statements are inconsistent.
d. The statements could still be invalid.
e. The second line in the truth table must be completed.