Question 1

Given the argument: S ∨ L / L ⊃ ∼ S // S ∨ ∼ L
This argument is:

Accepted Answer

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

Question 2

Honda reduces inventory if and only if Mercedes does not introduce a new model, unless Toyota closes a factory.

Accepted Answer

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

Question 3

Williams hires new faculty if either Smith increases enrollment or Amherst does not raise tuition, but Tulane reduces class size only if neither Rice expands course offerings nor Baylor offers new scholarships.

Accepted Answer

A)  [W ⊃ ∼(S ∨ 
A) ] ∨ [T ⊃ ∼(R ∨ 
B) ] 
B)  [T ⊃ ∼(R ∨ 
B) ] ⊃ [(S ∨ ∼
A)  ⊃ W] 
C)  [W ⊃ (S ∨ ∼
A) ] • [∼(R ∨ 
B)  ⊃ T] 
D)  [(S ∨ ∼
A)  ⊃ W] • [T ⊃ ∼(R ∨ 
B) ] 
E)  [(S ∨ ∼
A)  ⊃ W] • [T ⊃ (∼R ∨ ∼
B) ] 
A)  [W ⊃ ∼(S ∨ 
A) ] ∨ [T ⊃ ∼(R ∨ 
B) ] 
B)  [T ⊃ ∼(R ∨ 
B) ] ⊃ [(S ∨ ∼
A)  ⊃ W] 
C)  [W ⊃ (S ∨ ∼
A) ] • [∼(R ∨ 
B)  ⊃ T] 
D)  [(S ∨ ∼
A)  ⊃ W] • [T ⊃ ∼(R ∨ 
B) ] 
E)  [(S ∨ ∼
A)  ⊃ W] • [T ⊃ (∼R ∨ ∼
B) ]

Question 4

The truth table for Statement 1F 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.

Question 5

Given the argument: S ⊃ W / C ⊃ L / (M • ∼L) ∨ (D • ∼W) / C ∨ S // D • M
This argument is:

Accepted Answer

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

Question 6

Statement 1C
Given the following statement:
(H ∨ ∼ K) ≡ (K ⊃ H)
-Statement 1C is:

Accepted Answer

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

Question 7

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 8

Movado's offering an ivory dial is a sufficient condition for Breitling's having a ruby model if Gucci's offering a better warranty is a necessary condition for Fossil's being water resistant.

Accepted Answer

A)  (M ⊃ 
B)  ⊃ (F ⊃ G) 
B)  (B ⊃ M) ⊃ (G ⊃ F) 
C)  (G ⊃ F) ⊃ (B ⊃ M) 
D)  (F ⊃ G) ⊃ (M ⊃ 
B)  
E)  F ⊃ [G ⊃ (M ⊃ 
B) ] 
A)  (M ⊃ 
B)  ⊃ (F ⊃ G) 
B)  (B ⊃ M) ⊃ (G ⊃ F) 
C)  (G ⊃ F) ⊃ (B ⊃ M) 
D)  (F ⊃ G) ⊃ (M ⊃ 
B)  
E)  F ⊃ [G ⊃ (M ⊃ 
B) ]

Question 9

According to De Morgan's rule, ∼(P • Q) is logically equivalent to:

Accepted Answer

A)  P ∨ Q 
B)  ∼P • ∼Q 
C)  ∼P ∨ ∼Q 
D)  P • Q 
E)  P ≡ Q 
A)  P ∨ Q 
B)  ∼P • ∼Q 
C)  ∼P ∨ ∼Q 
D)  P • Q 
E)  P ≡ Q

Question 10

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

Accepted Answer

A) True 
 B)False

Question 11

Glamour's hiring models is a sufficient condition for Cosmo's adding new features unless Playboy's deleting its centerfold is a necessary condition for Maxim's changing its image.

Accepted Answer

A)  (C ⊃ G) ⊃ (P ⊃ M) 
B)  G ⊃ [C ∨ (P ⊃ M)] 
C)  (C ⊃ G) ∨ (P ⊃ M) 
D)  (G ⊃ 
C)  ⊃ (M ⊃ P) 
E)  (G ⊃ 
C)  ∨ (M ⊃ P) 
A)  (C ⊃ G) ⊃ (P ⊃ M) 
B)  G ⊃ [C ∨ (P ⊃ M)] 
C)  (C ⊃ G) ∨ (P ⊃ M) 
D)  (G ⊃ 
C)  ⊃ (M ⊃ P) 
E)  (G ⊃ 
C)  ∨ (M ⊃ P)

Question 12

Statement 1G
Given the following statement:
(A • B) ≡ (∼A • ∼B)
-The truth table for Statement 1G has how many lines?

Accepted Answer

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

Question 13

Given the argument: (K • ∼ C) ⊃ ∼(P • R) / J ⊃ (K • P) / A ⊃ (P • R) // (A • J) ⊃ C
This argument is:

Accepted Answer

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

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.

Question 15

Given the statements: R ⊃ M / C ⊃ E / M ⊃ ∼ E / R • C
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 16

Given the statement: (K ≡ ∼ S) • ∼ (S ⊃ ∼ K)
This statement is:

Accepted Answer

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

Question 17

Budget lowers rates unless Hertz and Thrifty do not overhaul operations.

Accepted Answer

A)  B ∨ (∼H • ∼T) 
B)  B ∨ ∼(H • T) 
C)  B ⊃ (∼H • ∼T) 
D)  (∼H • ∼T) ⊃ B 
E)  (B ∨ ∼H) • ∼T 
A)  B ∨ (∼H • ∼T) 
B)  B ∨ ∼(H • T) 
C)  B ⊃ (∼H • ∼T) 
D)  (∼H • ∼T) ⊃ B 
E)  (B ∨ ∼H) • ∼T

Question 18

Piaget and Nautica do not have a sapphire watch unless Breitling's having a diamond watch is a sufficient and necessary condition for either Cartier's offering multiple dials or Gucci's selling a self-winder.

Accepted Answer

A)  ∼(P • N) ∨ [(C ∨ G) ≡ B] 
B)  (∼P • ∼N) ∨ [(B ⊃ 
C)  • (G ⊃ 
B) ] 
C)  (∼P • ∼N) ∨ [(B ≡ (C ∨ G)] 
D)  (∼P • ∼N) ⊃ [(B ≡ (C ∨ G)] 
E)  [(B ≡ (C ∨G)] ⊃ (∼P • ∼N) 
A)  ∼(P • N) ∨ [(C ∨ G) ≡ B] 
B)  (∼P • ∼N) ∨ [(B ⊃ 
C)  • (G ⊃ 
B) ] 
C)  (∼P • ∼N) ∨ [(B ≡ (C ∨ G)] 
D)  (∼P • ∼N) ⊃ [(B ≡ (C ∨ G)] 
E)  [(B ≡ (C ∨G)] ⊃ (∼P • ∼N)

Question 19

Proposition 1E
Given the following proposition:
∼{[(Y ≡ ∼ A) ⊃ (∼ X ∨ Y)] • (∼ B ∨ ∼ X)}
-Given that A and B are true and X and Y are false, determine the truth value of Proposition 1E.

Accepted Answer

A) True 
 B)False

Question 20

Proposition 2B
Given the following proposition:
[(A ⊃ Y) ≡ (B ⊃ ∼X)] ∨ ∼[(B • ∼ X) ≡ (Y • A)]
-In Proposition 2B, the main operator is a:

Accepted Answer

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

Given the argument: S ∨ L / L ⊃ ∼ S // S ∨ ∼ L This argument is:

Honda reduces inventory if and only if Mercedes does not introduce a new model, unless Toyota closes a factory.

Williams hires new faculty if either Smith increases enrollment or Amherst does not raise tuition, but Tulane reduces class size only if neither Rice expands course offerings nor Baylor offers new scholarships.

The truth table for Statement 1F has how many lines?

Given the argument: S ⊃ W / C ⊃ L / (M • ∼L) ∨ (D • ∼W) / C ∨ S // D • M This argument is:

Statement 1C Given the following statement: (H ∨ ∼ K) ≡ (K ⊃ H) -Statement 1C is:

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.

Movado's offering an ivory dial is a sufficient condition for Breitling's having a ruby model if Gucci's offering a better warranty is a necessary condition for Fossil's being water resistant.

According to De Morgan's rule, ∼(P • Q) is logically equivalent to:

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

Glamour's hiring models is a sufficient condition for Cosmo's adding new features unless Playboy's deleting its centerfold is a necessary condition for Maxim's changing its image.

Statement 1G Given the following statement: (A • B) ≡ (∼A • ∼B) -The truth table for Statement 1G has how many lines?

Given the argument: (K • ∼ C) ⊃ ∼(P • R) / J ⊃ (K • P) / A ⊃ (P • R) // (A • J) ⊃ C This argument is:

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

Given the statements: R ⊃ M / C ⊃ E / M ⊃ ∼ E / R • C These statements are:

Given the statement: (K ≡ ∼ S) • ∼ (S ⊃ ∼ K) This statement is:

Budget lowers rates unless Hertz and Thrifty do not overhaul operations.

Piaget and Nautica do not have a sapphire watch unless Breitling's having a diamond watch is a sufficient and necessary condition for either Cartier's offering multiple dials or Gucci's selling a self-winder.

Proposition 1E Given the following proposition: ∼{[(Y ≡ ∼ A) ⊃ (∼ X ∨ Y)] • (∼ B ∨ ∼ X)} -Given that A and B are true and X and Y are false, determine the truth value of Proposition 1E.

Proposition 2B Given the following proposition: [(A ⊃ Y) ≡ (B ⊃ ∼X)] ∨ ∼[(B • ∼ X) ≡ (Y • A)] -In Proposition 2B, the main operator is a:

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 ∨ L / L ⊃ ∼ S // S ∨ ∼ L This argument is:

Honda reduces inventory if and only if Mercedes does not introduce a new model, unless Toyota closes a factory.

Williams hires new faculty if either Smith increases enrollment or Amherst does not raise tuition, but Tulane reduces class size only if neither Rice expands course offerings nor Baylor offers new scholarships.

The truth table for Statement 1F has how many lines?

Given the argument: S ⊃ W / C ⊃ L / (M • ∼L) ∨ (D • ∼W) / C ∨ S // D • M This argument is:

Statement 1C Given the following statement: (H ∨ ∼ K) ≡ (K ⊃ H) -Statement 1C is:

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.

Movado's offering an ivory dial is a sufficient condition for Breitling's having a ruby model if Gucci's offering a better warranty is a necessary condition for Fossil's being water resistant.

According to De Morgan's rule, ∼(P • Q) is logically equivalent to:

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

Glamour's hiring models is a sufficient condition for Cosmo's adding new features unless Playboy's deleting its centerfold is a necessary condition for Maxim's changing its image.

Statement 1G Given the following statement: (A • B) ≡ (∼A • ∼B) -The truth table for Statement 1G has how many lines?

Given the argument: (K • ∼ C) ⊃ ∼(P • R) / J ⊃ (K • P) / A ⊃ (P • R) // (A • J) ⊃ C This argument is:

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

Given the statements: R ⊃ M / C ⊃ E / M ⊃ ∼ E / R • C These statements are:

Given the statement: (K ≡ ∼ S) • ∼ (S ⊃ ∼ K) This statement is:

Budget lowers rates unless Hertz and Thrifty do not overhaul operations.

Piaget and Nautica do not have a sapphire watch unless Breitling's having a diamond watch is a sufficient and necessary condition for either Cartier's offering multiple dials or Gucci's selling a self-winder.

Proposition 1E Given the following proposition: ∼{[(Y ≡ ∼ A) ⊃ (∼ X ∨ Y)] • (∼ B ∨ ∼ X)} -Given that A and B are true and X and Y are false, determine the truth value of Proposition 1E.

Proposition 2B Given the following proposition: [(A ⊃ Y) ≡ (B ⊃ ∼X)] ∨ ∼[(B • ∼ X) ≡ (Y • A)] -In Proposition 2B, the main operator is a:

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