Question 1

If a group of statements are consistent, this means:

Accepted Answer

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. 
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.

Question 2

If National's improving efficiency implies that Enterprise reorganizes, then Avis buys new cars.

Accepted Answer

A)  (N ⊃ E ⊃ 
A)  
B)  N ⊃ (E ⊃ 
A)  
C)  (N ⊃ 
E)  ⊃ A 
D)  A ⊃ (N ⊃ 
E)  
E)  (E ⊃ N) ⊃ A 
A)  (N ⊃ E ⊃ 
A)  
B)  N ⊃ (E ⊃ 
A)  
C)  (N ⊃ 
E)  ⊃ A 
D)  A ⊃ (N ⊃ 
E)  
E)  (E ⊃ N) ⊃ A

Question 3

Given the pair of statements: Q ≡ ∼ A and A • ∼ Q
These statements are:

Accepted Answer

A)  Consistent. 
B)  Inconsistent. 
C)  Valid. 
D)  Contradictory. 
E)  Logically equivalent. 
A)  Consistent. 
B)  Inconsistent. 
C)  Valid. 
D)  Contradictory. 
E)  Logically equivalent.

Question 4

The wedge operator is used to translate:

Accepted Answer

A)  "Nevertheless." 
B)  "Moreover." 
C)  "Unless." 
D)  "Implies." 
E)  "Provided that." 
A)  "Nevertheless." 
B)  "Moreover." 
C)  "Unless." 
D)  "Implies." 
E)  "Provided that."

Question 5

Harp is soothing if and only if both Miller is not zesty and Coors is not smooth.

Accepted Answer

A)  H ≡ ∼(M • 
C)  
B)  (H ⊃ ∼M) • (H ⊃ ∼
C)  
C)  H ≡ (∼M • ∼
C)  
D)  (H ≡ ∼M) • (H ≡ ∼
C)  
E)  H ≡ (M • 
C)  
A)  H ≡ ∼(M • 
C)  
B)  (H ⊃ ∼M) • (H ⊃ ∼
C)  
C)  H ≡ (∼M • ∼
C)  
D)  (H ≡ ∼M) • (H ≡ ∼
C)  
E)  H ≡ (M • 
C)

Question 6

Statement 2I
Given the following statement:
(L • ∼ E) ≡ (E • ∼ L)
-Statement 2I is:

Accepted Answer

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

Question 7

Southwest expands routes if either American does not hire pilots or United does not lower fares.

Accepted Answer

A)  ∼(A ∨ U) ⊃ S 
B)  (∼A • ∼U) ⊃ S 
C)  S ⊃ (∼A ∨ ∼U) 
D)  (S ⊃ ∼A ∨ ∼U) 
E)  (∼A ∨ ∼U) ⊃ S 
A)  ∼(A ∨ U) ⊃ S 
B)  (∼A • ∼U) ⊃ S 
C)  S ⊃ (∼A ∨ ∼U) 
D)  (S ⊃ ∼A ∨ ∼U) 
E)  (∼A ∨ ∼U) ⊃ S

Question 8

JetBlue buys planes if and only if both Delta does not advertise a sale and Southwest does not expand routes.

Accepted Answer

A)  J ≡ ∼(D • S) 
B)  J ⊃ (∼D • ∼S) 
C)  J ≡ (∼D • ∼S) 
D)  ∼(D ∨ S) ⊃ J 
E)  J ∨ (∼D • ∼S) 
A)  J ≡ ∼(D • S) 
B)  J ⊃ (∼D • ∼S) 
C)  J ≡ (∼D • ∼S) 
D)  ∼(D ∨ S) ⊃ J 
E)  J ∨ (∼D • ∼S)

Question 9

D ⊃ ∼N

Accepted Answer

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

Question 10

Given the statements: Q ⊃ (N ∨ S) / N ⊃ (L ⊃ B) / (S ∨ E) ⊃ (Q ⊃ B) / Q ≡ ∼ B
These statements are:

Accepted Answer

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

Question 11

Given the argument: Q ∨ ∼ S / ∼(N • A) / S ∨ A / (P • N) ∨ (G • Q) // P • G
This argument is:

Accepted Answer

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

Question 12

Given the statements: R ⊃ (M ∨ ∼ C) / (P ∨ U) ⊃ C / M ⊃ ∼ P / R ≡ U
These statements are:

Accepted Answer

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

Question 13

Gucci features stainless steel; also, Fossil is water resistant given that Cartier offers a stop watch.

Accepted Answer

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

Question 14

Given the pair of statements: Q ≡ N and (N • ∼ Q) ∨ (Q • ∼ N)
These statements are:

Accepted Answer

A)  Contradictory. 
B)  Logically equivalent. 
C)  Inconsistent. 
D)  Consistent. 
E)  Valid. 
A)  Contradictory. 
B)  Logically equivalent. 
C)  Inconsistent. 
D)  Consistent. 
E)  Valid.

Question 15

Delta advertises a sale and either United lowers fares or American hires pilots.

Accepted Answer

A)  D • (U ∨ 
A)  
B)  D ∨ (U • 
A)  
C)  D • U ∨ A 
D)  (D • U) ∨ A 
E)  D ∨ (U • 
A) . 
A)  D • (U ∨ 
A)  
B)  D ∨ (U • 
A)  
C)  D • U ∨ A 
D)  (D • U) ∨ A 
E)  D ∨ (U • 
A) .

Question 16

Given the argument: K ∨ E / E ⊃ ∼ K // K ≡ ∼ E
This argument is:

Accepted Answer

A)  Invalid; fails in 2nd line. 
B)  Valid. 
C)  Invalid; fails in 1st line. 
D)  Invalid; fails in 4th line. 
E)  Invalid; fails in 3rd line. 
A)  Invalid; fails in 2nd line. 
B)  Valid. 
C)  Invalid; fails in 1st line. 
D)  Invalid; fails in 4th line. 
E)  Invalid; fails in 3rd line.

Question 17

L

Accepted Answer

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

Question 18

Given the argument: M ⊃ J / ∼ J ⊃ R // (M ∨ ∼ R) ⊃ J
This argument is:

Accepted Answer

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. 
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.

Question 19

Piaget has a gold watch only if both Seiko has leather bands and Breitling has a diamond model.

Accepted Answer

A)  P ⊃ (S • 
B)  
B)  (S • 
B)  ∨ P 
C)  (S • 
B)  ⊃ P 
D)  (S • 
B)  ≡ P 
E)  S • (B ⊃ P) 
A)  P ⊃ (S • 
B)  
B)  (S • 
B)  ∨ P 
C)  (S • 
B)  ⊃ P 
D)  (S • 
B)  ≡ P 
E)  S • (B ⊃ P)

Question 20

Given the argument: Q ⊃ (C • N) / S ⊃ (C ∨ N) / Q ∨ S / N ⊃ K // K • C
This argument is:

Accepted Answer

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

If a group of statements are consistent, this means:

If National's improving efficiency implies that Enterprise reorganizes, then Avis buys new cars.

Given the pair of statements: Q ≡ ∼ A and A • ∼ Q These statements are:

The wedge operator is used to translate:

Harp is soothing if and only if both Miller is not zesty and Coors is not smooth.

Statement 2I Given the following statement: (L • ∼ E) ≡ (E • ∼ L) -Statement 2I is:

Southwest expands routes if either American does not hire pilots or United does not lower fares.

JetBlue buys planes if and only if both Delta does not advertise a sale and Southwest does not expand routes.

D ⊃ ∼N

Given the statements: Q ⊃ (N ∨ S) / N ⊃ (L ⊃ B) / (S ∨ E) ⊃ (Q ⊃ B) / Q ≡ ∼ B These statements are:

Given the argument: Q ∨ ∼ S / ∼(N • A) / S ∨ A / (P • N) ∨ (G • Q) // P • G This argument is:

Given the statements: R ⊃ (M ∨ ∼ C) / (P ∨ U) ⊃ C / M ⊃ ∼ P / R ≡ U These statements are:

Gucci features stainless steel; also, Fossil is water resistant given that Cartier offers a stop watch.

Given the pair of statements: Q ≡ N and (N • ∼ Q) ∨ (Q • ∼ N) These statements are:

Delta advertises a sale and either United lowers fares or American hires pilots.

Given the argument: K ∨ E / E ⊃ ∼ K // K ≡ ∼ E This argument is:

L

Given the argument: M ⊃ J / ∼ J ⊃ R // (M ∨ ∼ R) ⊃ J This argument is:

Piaget has a gold watch only if both Seiko has leather bands and Breitling has a diamond model.

Given the argument: Q ⊃ (C • N) / S ⊃ (C ∨ N) / Q ∨ S / N ⊃ K // K • C 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

If a group of statements are consistent, this means:

If National's improving efficiency implies that Enterprise reorganizes, then Avis buys new cars.

Given the pair of statements: Q ≡ ∼ A and A • ∼ Q These statements are:

The wedge operator is used to translate:

Harp is soothing if and only if both Miller is not zesty and Coors is not smooth.

Statement 2I Given the following statement: (L • ∼ E) ≡ (E • ∼ L) -Statement 2I is:

Southwest expands routes if either American does not hire pilots or United does not lower fares.

JetBlue buys planes if and only if both Delta does not advertise a sale and Southwest does not expand routes.

D ⊃ ∼N

Given the statements: Q ⊃ (N ∨ S) / N ⊃ (L ⊃ B) / (S ∨ E) ⊃ (Q ⊃ B) / Q ≡ ∼ B These statements are:

Given the argument: Q ∨ ∼ S / ∼(N • A) / S ∨ A / (P • N) ∨ (G • Q) // P • G This argument is:

Given the statements: R ⊃ (M ∨ ∼ C) / (P ∨ U) ⊃ C / M ⊃ ∼ P / R ≡ U These statements are:

Gucci features stainless steel; also, Fossil is water resistant given that Cartier offers a stop watch.

Given the pair of statements: Q ≡ N and (N • ∼ Q) ∨ (Q • ∼ N) These statements are:

Delta advertises a sale and either United lowers fares or American hires pilots.

Given the argument: K ∨ E / E ⊃ ∼ K // K ≡ ∼ E This argument is:

L

Given the argument: M ⊃ J / ∼ J ⊃ R // (M ∨ ∼ R) ⊃ J This argument is:

Piaget has a gold watch only if both Seiko has leather bands and Breitling has a diamond model.

Given the argument: Q ⊃ (C • N) / S ⊃ (C ∨ N) / Q ∨ S / N ⊃ K // K • C 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