Question 1

Given the argument: S ⊃ (K ∨ ∼ S) / K ⊃ S // S ≡ K
This argument is:

Accepted Answer

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

Question 2

Given the argument: E ⊃ J / B ⊃ Q / D ⊃ (J • ∼ Q) // (E • B) ≡ D
This argument is:

Accepted Answer

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

Question 3

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 4

Given the statements: H ⊃ E / M ⊃ R / (M • E) ⊃ G / (R • G) ⊃ E / M ∨ E
These statements are:

Accepted Answer

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

Question 5

Not both Hertz runs a sale and Thrifty lays off workers if either Avis buys new cars or Budget lowers rates.

Accepted Answer

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) 
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)

Question 6

Cosmo raises its price if and only if both Redbook increases circulation and Glamour hires new writers, but either Shape or Health expands coverage if Forbes adds new features.

Accepted Answer

A)  [(C ≡ R) • G] • [(F ⊃ S) ∨ H] 
B)  (R • G) ≡ [(C ⊃ F) ⊃ (S ∨ H)] 
C)  [C ≡ (R • G)] • [F ⊃ (S ∨ H)] 
D)  [C ⊃ (R • G)] • [F ≡ (S ∨ H)] 
E)  C ≡ {(R • G) • [F ⊃ (S ∨ H)]} 
A)  [(C ≡ R) • G] • [(F ⊃ S) ∨ H] 
B)  (R • G) ≡ [(C ⊃ F) ⊃ (S ∨ H)] 
C)  [C ≡ (R • G)] • [F ⊃ (S ∨ H)] 
D)  [C ⊃ (R • G)] • [F ≡ (S ∨ H)] 
E)  C ≡ {(R • G) • [F ⊃ (S ∨ H)]}

Question 7

JetBlue buys planes unless neither Frontier improves service nor United lowers fares.

Accepted Answer

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

Question 8

Movado and Nautica offer a black dial if and only if Piaget has a gold watch.

Accepted Answer

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

Question 9

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 10

L ∼N ⊃ L
∼N

Accepted Answer

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

Question 11

Given the statements: A ⊃ (B • C) / B ⊃ (D ∨ ∼ E) / C ⊃ (E ∨ ∼ D) / A • E.
These statements are:

Accepted Answer

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

Question 12

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.

Accepted Answer

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

Question 13

Given the pair of statements: C • ∼ L and L • ∼ C
These statements are:

Accepted Answer

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

Question 14

Statement 1D
Given the following statement:
∼ (H ⊃ A) ∨ (A ⊃ H)
-The truth table for Statement 1D has how many lines?

Accepted Answer

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

Given the argument: S ⊃ (K ∨ ∼ S) / K ⊃ S // S ≡ K This argument is:

Given the argument: E ⊃ J / B ⊃ Q / D ⊃ (J • ∼ Q) // (E • B) ≡ D This argument is:

If a group of statements are consistent, this means:

Given the statements: H ⊃ E / M ⊃ R / (M • E) ⊃ G / (R • G) ⊃ E / M ∨ E These statements are:

Not both Hertz runs a sale and Thrifty lays off workers if either Avis buys new cars or Budget lowers rates.

Cosmo raises its price if and only if both Redbook increases circulation and Glamour hires new writers, but either Shape or Health expands coverage if Forbes adds new features.

JetBlue buys planes unless neither Frontier improves service nor United lowers fares.

Movado and Nautica offer a black dial if and only if Piaget has a gold watch.

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

L ∼N ⊃ L ∼N

Given the statements: A ⊃ (B • C) / B ⊃ (D ∨ ∼ E) / C ⊃ (E ∨ ∼ D) / A • E. These statements are:

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.

Given the pair of statements: C • ∼ L and L • ∼ C These statements are:

Statement 1D Given the following statement: ∼ (H ⊃ A) ∨ (A ⊃ H) -The truth table for Statement 1D has how many lines?

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

Given the argument: S ⊃ (K ∨ ∼ S) / K ⊃ S // S ≡ K This argument is:

Given the argument: E ⊃ J / B ⊃ Q / D ⊃ (J • ∼ Q) // (E • B) ≡ D This argument is:

If a group of statements are consistent, this means:

Given the statements: H ⊃ E / M ⊃ R / (M • E) ⊃ G / (R • G) ⊃ E / M ∨ E These statements are:

Not both Hertz runs a sale and Thrifty lays off workers if either Avis buys new cars or Budget lowers rates.

Cosmo raises its price if and only if both Redbook increases circulation and Glamour hires new writers, but either Shape or Health expands coverage if Forbes adds new features.

JetBlue buys planes unless neither Frontier improves service nor United lowers fares.

Movado and Nautica offer a black dial if and only if Piaget has a gold watch.

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

L ∼N ⊃ L ∼N

Given the statements: A ⊃ (B • C) / B ⊃ (D ∨ ∼ E) / C ⊃ (E ∨ ∼ D) / A • E. These statements are:

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.

Given the pair of statements: C • ∼ L and L • ∼ C These statements are:

Statement 1D Given the following statement: ∼ (H ⊃ A) ∨ (A ⊃ H) -The truth table for Statement 1D has how many lines?

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