Question 1

Either Safeco reduces premiums and Geico cuts costs or Farmers hires agents.

Accepted Answer

A)  S • (G ∨ F) 
B)  (S • G) ⊃ F 
C)  (S • G) ∨ F 
D)  (S ∨ G) • F 
E)  S ∨ (G • F) 
A)  S • (G ∨ F) 
B)  (S • G) ⊃ F 
C)  (S • G) ∨ F 
D)  (S ∨ G) • F 
E)  S ∨ (G • F) C

Question 2

Hertz runs a sale or both Avis buys new cars and Budget lowers rates.

Accepted Answer

A)  H ∨ A • B 
B)  H ∨ (A • 
B)  
C)  (H ∨ 
A)  • B 
D)  H • (A ∨ 
B)  
E)  H • A ∨ B 
A)  H ∨ A • B 
B)  H ∨ (A • 
B)  
C)  (H ∨ 
A)  • B 
D)  H • (A ∨ 
B)  
E)  H • A ∨ B B

Question 3

Statement 1B
(R • B) ≡ (B ⊃ ∼ R)
-The truth table for Statement 1B has how many lines?

Accepted Answer

A)  Six. 
B)  Four. 
C)  Two. 
D)  Eight. 
E)  Nine. 
A)  Six. 
B)  Four. 
C)  Two. 
D)  Eight. 
E)  Nine. B

Question 4

Statement 1D
Given the following statement:
∼ (H ⊃ A) ∨ (A ⊃ H)
-Statement 1D is:

Accepted Answer

A)  Self-contradictory. 
B)  Inconsistent. 
C)  Consistent. 
D)  Tautologous. 
E)  Contingent. 
A)  Self-contradictory. 
B)  Inconsistent. 
C)  Consistent. 
D)  Tautologous. 
E)  Contingent.

Question 5

In Proposition 2I, the main operator is a:

Accepted Answer

A)  Tilde. 
B)  Wedge. 
C)  Horseshoe. 
D)  Triple bar. 
E)  Dot. 
A)  Tilde. 
B)  Wedge. 
C)  Horseshoe. 
D)  Triple bar. 
E)  Dot.

Question 6

(∼G ∨ E) • (R ∨ M)

Accepted Answer

A)  MT-valid. 
B)  Invalid. 
C)  DA-invalid. 
D)  MP-valid. 
E)  AC-invalid. 
A)  MT-valid. 
B)  Invalid. 
C)  DA-invalid. 
D)  MP-valid. 
E)  AC-invalid.

Question 7

Thrifty lays off workers only if neither National improves efficiency nor Enterprise reorganizes.

Accepted Answer

A)  T ⊃ ∼(N ∨ 
E)  
B)  ∼(N ∨ 
E)  ⊃ T 
C)  T ⊃ (∼N ∨ ∼T) 
D)  (∼N ∨ ∼
E)  ⊃ T 
E)  T ≡ ∼(N ∨ 
E)  
A)  T ⊃ ∼(N ∨ 
E)  
B)  ∼(N ∨ 
E)  ⊃ T 
C)  T ⊃ (∼N ∨ ∼T) 
D)  (∼N ∨ ∼
E)  ⊃ T 
E)  T ≡ ∼(N ∨ 
E)

Question 8

Given the statement: ∼ (S • ∼ D) ∨ (D ⊃ S)
This statement is:

Accepted Answer

A)  Valid. 
B)  Tautologous. 
C)  Inconsistent. 
D)  Contingent. 
E)  Self-contradictory. 
A)  Valid. 
B)  Tautologous. 
C)  Inconsistent. 
D)  Contingent. 
E)  Self-contradictory.

Question 9

Chrysler increases sales only if Honda reduces inventory, provided that Nissan does not lay off workers.

Accepted Answer

A)  (C ≡ H) ⊃ ∼N 
B)  (C ⊃ H) ⊃ ∼N 
C)  (H ⊃ 
C)  ⊃ ∼N 
D)  ∼N ⊃ (H ⊃ 
C)  
E)  ∼N ⊃ (C ⊃ H) 
A)  (C ≡ H) ⊃ ∼N 
B)  (C ⊃ H) ⊃ ∼N 
C)  (H ⊃ 
C)  ⊃ ∼N 
D)  ∼N ⊃ (H ⊃ 
C)  
E)  ∼N ⊃ (C ⊃ H)

Question 10

Given the statements: R ⊃ (Q ∨ ∼ N) / Q ⊃ (U ⊃ ∼ B) / B ⊃ (N • U) / R • B
These statements are:

Accepted Answer

A)  Inconsistent. 
B)  Invalid. 
C)  Consistent. 
D)  Logically equivalent. 
E)  Tautologous. 
A)  Inconsistent. 
B)  Invalid. 
C)  Consistent. 
D)  Logically equivalent. 
E)  Tautologous.

Question 11

Given the argument: (A • B) ∨ (C • D) / E ⊃ ∼ B / F ⊃ ∼ D / E ∨ F // A • C.
This argument is:

Accepted Answer

A)  Valid. 
B)  Invalid. 
C)  Uncogent. 
D)  Cogent. 
E)  Sound. 
A)  Valid. 
B)  Invalid. 
C)  Uncogent. 
D)  Cogent. 
E)  Sound.

Question 12

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.

Accepted Answer

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)] 
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)]

Question 13

∼G ∨ ∼B

Accepted Answer

A)  Disjunctive syllogism. 
B)  Invalid. 
C)  Denying the antecedent. 
D)  Affirming the consequent. 
E)  Modus tollens. 
A)  Disjunctive syllogism. 
B)  Invalid. 
C)  Denying the antecedent. 
D)  Affirming the consequent. 
E)  Modus tollens.

Question 14

Given the statements: ∼ S ⊃ D / K ⊃ S / D ⊃ K / R ≡ ∼(S • C) / R ≡ C
These statements are:

Accepted Answer

A)  Contradictory. 
B)  Tautologous. 
C)  Consistent. 
D)  Inconsistent. 
E)  Valid. 
A)  Contradictory. 
B)  Tautologous. 
C)  Consistent. 
D)  Inconsistent. 
E)  Valid.

Question 15

Statement 2A
Given the following statement:
(G ⊃ ∼ Q) ≡ ∼(Q • G)
-Statement 2A is:

Accepted Answer

A)  Consistent. 
B)  Self-contradictory. 
C)  Tautologous. 
D)  Contingent. 
E)  Logically equivalent. 
A)  Consistent. 
B)  Self-contradictory. 
C)  Tautologous. 
D)  Contingent. 
E)  Logically equivalent.

Question 16

If Tissot has luminous hands, then if either Rado advertises a calendar model or Fossil is water resistant, then Gucci features stainless steel.

Accepted Answer

A)  (R ∨ F) ⊃ (T ⊃ G) 
B)  (R ⊃ T) ⊃ (F ⊃ G) 
C)  [T ⊃ (R ∨ F)] ⊃ G 
D)  T ⊃ [(R ⊃ G) ∨ (F ⊃ G)] 
E)  T ⊃ [(R ∨ F) ⊃ G] 
A)  (R ∨ F) ⊃ (T ⊃ G) 
B)  (R ⊃ T) ⊃ (F ⊃ G) 
C)  [T ⊃ (R ∨ F)] ⊃ G 
D)  T ⊃ [(R ⊃ G) ∨ (F ⊃ G)] 
E)  T ⊃ [(R ∨ F) ⊃ G]

Question 17

S ∨ ∼T

Accepted Answer

A)  DA-invalid. 
B)  CD-valid. 
C)  Invalid. 
D)  DD-valid. 
E)  CD-invalid. 
A)  DA-invalid. 
B)  CD-valid. 
C)  Invalid. 
D)  DD-valid. 
E)  CD-invalid.

Question 18

∼A ⊃ ∼H

Accepted Answer

A)  DD-valid. 
B)  MP-valid. 
C)  CD-valid. 
D)  Invalid. 
E)  HS-valid. 
A)  DD-valid. 
B)  MP-valid. 
C)  CD-valid. 
D)  Invalid. 
E)  HS-valid.

Question 19

Proposition 2E
Given the following proposition:
[∼ (A ∨ Y) ≡ (∼ X ⊃ B)] ∨ [∼ (Y • ∼ B) ⊃ (X ⊃ ∼ A)]
-Given that A and B are true and X and Y are false, determine the truth value of Proposition 2E.

Accepted Answer

A) True 
 B)False

Question 20

Given the argument: R ⊃ D / D ⊃ (N ∨ S) / S ⊃ (P ∨ N) / N ⊃ R // R ≡ N
This argument is:

Accepted Answer

A)  Uncogent. 
B)  Invalid. 
C)  Sound. 
D)  Cogent. 
E)  Valid. 
A)  Uncogent. 
B)  Invalid. 
C)  Sound. 
D)  Cogent. 
E)  Valid.

Either Safeco reduces premiums and Geico cuts costs or Farmers hires agents.

Hertz runs a sale or both Avis buys new cars and Budget lowers rates.

Statement 1B (R • B) ≡ (B ⊃ ∼ R) -The truth table for Statement 1B has how many lines?

Statement 1D Given the following statement: ∼ (H ⊃ A) ∨ (A ⊃ H) -Statement 1D is:

In Proposition 2I, the main operator is a:

(∼G ∨ E) • (R ∨ M)

Thrifty lays off workers only if neither National improves efficiency nor Enterprise reorganizes.

Given the statement: ∼ (S • ∼ D) ∨ (D ⊃ S) This statement is:

Chrysler increases sales only if Honda reduces inventory, provided that Nissan does not lay off workers.

Given the statements: R ⊃ (Q ∨ ∼ N) / Q ⊃ (U ⊃ ∼ B) / B ⊃ (N • U) / R • B These statements are:

Given the argument: (A • B) ∨ (C • D) / E ⊃ ∼ B / F ⊃ ∼ D / E ∨ F // A • C. This argument is:

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.

∼G ∨ ∼B

Given the statements: ∼ S ⊃ D / K ⊃ S / D ⊃ K / R ≡ ∼(S • C) / R ≡ C These statements are:

Statement 2A Given the following statement: (G ⊃ ∼ Q) ≡ ∼(Q • G) -Statement 2A is:

If Tissot has luminous hands, then if either Rado advertises a calendar model or Fossil is water resistant, then Gucci features stainless steel.

S ∨ ∼T

∼A ⊃ ∼H

Proposition 2E Given the following proposition: [∼ (A ∨ Y) ≡ (∼ X ⊃ B)] ∨ [∼ (Y • ∼ B) ⊃ (X ⊃ ∼ A)] -Given that A and B are true and X and Y are false, determine the truth value of Proposition 2E.

Given the argument: R ⊃ D / D ⊃ (N ∨ S) / S ⊃ (P ∨ N) / N ⊃ R // R ≡ N This argument is:

Basic Concepts

Language: Meaning and Definition

Informal Fallacies

Categorical Propositions

Categorical Syllogisms

Natural Deduction in Propositional Logic

Predicate Logic

Analogy and Legal and Moral Reasoning

Causality and Mills Methods

Probability

Statistical Reasoning

Hypotheticalscientific Reasoning

Science and Superstition

Filters

Exam 6: Propositional Logic

Either Safeco reduces premiums and Geico cuts costs or Farmers hires agents.

Hertz runs a sale or both Avis buys new cars and Budget lowers rates.

Statement 1B (R • B) ≡ (B ⊃ ∼ R) -The truth table for Statement 1B has how many lines?

Statement 1D Given the following statement: ∼ (H ⊃ A) ∨ (A ⊃ H) -Statement 1D is:

In Proposition 2I, the main operator is a:

(∼G ∨ E) • (R ∨ M)

Thrifty lays off workers only if neither National improves efficiency nor Enterprise reorganizes.

Given the statement: ∼ (S • ∼ D) ∨ (D ⊃ S) This statement is:

Chrysler increases sales only if Honda reduces inventory, provided that Nissan does not lay off workers.

Given the statements: R ⊃ (Q ∨ ∼ N) / Q ⊃ (U ⊃ ∼ B) / B ⊃ (N • U) / R • B These statements are:

Given the argument: (A • B) ∨ (C • D) / E ⊃ ∼ B / F ⊃ ∼ D / E ∨ F // A • C. This argument is:

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.

∼G ∨ ∼B

Given the statements: ∼ S ⊃ D / K ⊃ S / D ⊃ K / R ≡ ∼(S • C) / R ≡ C These statements are:

Statement 2A Given the following statement: (G ⊃ ∼ Q) ≡ ∼(Q • G) -Statement 2A is:

If Tissot has luminous hands, then if either Rado advertises a calendar model or Fossil is water resistant, then Gucci features stainless steel.

S ∨ ∼T

∼A ⊃ ∼H

Proposition 2E Given the following proposition: [∼ (A ∨ Y) ≡ (∼ X ⊃ B)] ∨ [∼ (Y • ∼ B) ⊃ (X ⊃ ∼ A)] -Given that A and B are true and X and Y are false, determine the truth value of Proposition 2E.

Given the argument: R ⊃ D / D ⊃ (N ∨ S) / S ⊃ (P ∨ N) / N ⊃ R // R ≡ N This argument is:

Basic Concepts

Language: Meaning and Definition

Informal Fallacies

Categorical Propositions

Categorical Syllogisms

Natural Deduction in Propositional Logic

Predicate Logic

Analogy and Legal and Moral Reasoning

Causality and Mills Methods

Probability

Statistical Reasoning

Hypotheticalscientific Reasoning

Science and Superstition

Filters