Question 1

Statement 1F
Given the following statement:
∼ [K ⊃ (N ⊃ K)]
-Statement 1F is:

Accepted Answer

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

Question 2

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.

Accepted Answer

A)  Disjunctive syllogism. 
B)  Destructive dilemma. 
C)  Pure hypothetical syllogism. 
D)  Modus ponens. 
E)  Invalid. 
A)  Disjunctive syllogism. 
B)  Destructive dilemma. 
C)  Pure hypothetical syllogism. 
D)  Modus ponens. 
E)  Invalid.

Question 3

K ∨ ∼B B
K

Accepted Answer

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

Question 4

Given the statements: P ⊃ (A ⊃ M) / (D ∨ K) ⊃ (M ⊃ H) / (A • ∼ H) ∨ ∼ D / P • D
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 5

If Fordham expands course offerings, then if Georgetown increases its endowment, then both Duke raises tuition and Tulane reduces class size.

Accepted Answer

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

Question 6

(∼H ⊃ K) • (H ⊃ ∼T)

Accepted Answer

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

Question 7

Progressive increases its territory if neither Safeco cuts costs nor Travelers runs an ad.

Accepted Answer

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

Question 8

Either Breitling has a diamond model and Rado advertises a calendar watch or Tissot has luminous hands.

Accepted Answer

A)  B ∨ (R • T) 
B)  (B ∨ R) • T 
C)  (B • R) ∨ T 
D)  B • R ∨ T 
E)  B • (R ∨ T) 
A)  B ∨ (R • T) 
B)  (B ∨ R) • T 
C)  (B • R) ∨ T 
D)  B • R ∨ T 
E)  B • (R ∨ T)

Question 9

Proposition 1H
Given the following proposition:
[(A ≡ ∼B) ∨ (X ⊃ Y)] • [(Y ⊃ A) ≡ ∼(X ∨ B)]
-In Proposition 1H, the main operator is a:

Accepted Answer

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

Question 10

Not both Playboy changes its image and Maxim changes its cover given that Glamour hires models.

Accepted Answer

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

Question 11

Given the argument: W ∨ ∼ S / E ∨ ∼ A / (K ∨ L) ≡ (A • S) // L ⊃ (E • W)
This argument is:

Accepted Answer

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

Question 12

∼Q ∨ S

Accepted Answer

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

Question 13

∼N ∨ A

Accepted Answer

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

Question 14

Given the argument: A ⊃ ∼B / B ∨ A // ∼B ≡ A.
This argument is:

Accepted Answer

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. 
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.

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

Given the pair of statements: ∼ (H ≡ R) and ∼ (R ⊃ ∼ H)
These statements are:

Accepted Answer

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

Question 17

Given the pair of statements: J ≡ ∼ M and (J • M) ∨ ∼(M ∨ J)
These statements are:

Accepted Answer

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

Question 18

Statement 2H
Given the following statement:
[N ∨ ∼ (K ∨ G)] ≡ [(G ⊃ N) • (K ⊃ N)]
-Statement 2H is:

Accepted Answer

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

Question 19

Given the statements: W ⊃ (E ∨ ∼ G) / A ⊃ (G ∨ ∼ E) / H ⊃ (A • W) / H • E
These statements are:

Accepted Answer

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

Question 20

Given the argument: K ⊃ (M ∨ ∼ H) / M ⊃ H / M ⊃ K // K ⊃ H
This argument is:

Accepted Answer

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

Statement 1F Given the following statement: ∼ [K ⊃ (N ⊃ K)] -Statement 1F is:

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.

K ∨ ∼B B K

Given the statements: P ⊃ (A ⊃ M) / (D ∨ K) ⊃ (M ⊃ H) / (A • ∼ H) ∨ ∼ D / P • D These statements are:

If Fordham expands course offerings, then if Georgetown increases its endowment, then both Duke raises tuition and Tulane reduces class size.

(∼H ⊃ K) • (H ⊃ ∼T)

Progressive increases its territory if neither Safeco cuts costs nor Travelers runs an ad.

Either Breitling has a diamond model and Rado advertises a calendar watch or Tissot has luminous hands.

Proposition 1H Given the following proposition: [(A ≡ ∼B) ∨ (X ⊃ Y)] • [(Y ⊃ A) ≡ ∼(X ∨ B)] -In Proposition 1H, the main operator is a:

Not both Playboy changes its image and Maxim changes its cover given that Glamour hires models.

Given the argument: W ∨ ∼ S / E ∨ ∼ A / (K ∨ L) ≡ (A • S) // L ⊃ (E • W) This argument is:

∼Q ∨ S

∼N ∨ A

Given the argument: A ⊃ ∼B / B ∨ A // ∼B ≡ A. This argument is:

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

Given the pair of statements: ∼ (H ≡ R) and ∼ (R ⊃ ∼ H) These statements are:

Given the pair of statements: J ≡ ∼ M and (J • M) ∨ ∼(M ∨ J) These statements are:

Statement 2H Given the following statement: [N ∨ ∼ (K ∨ G)] ≡ [(G ⊃ N) • (K ⊃ N)] -Statement 2H is:

Given the statements: W ⊃ (E ∨ ∼ G) / A ⊃ (G ∨ ∼ E) / H ⊃ (A • W) / H • E These statements are:

Given the argument: K ⊃ (M ∨ ∼ H) / M ⊃ H / M ⊃ K // K ⊃ H 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

Statement 1F Given the following statement: ∼ [K ⊃ (N ⊃ K)] -Statement 1F is:

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.

K ∨ ∼B B K

Given the statements: P ⊃ (A ⊃ M) / (D ∨ K) ⊃ (M ⊃ H) / (A • ∼ H) ∨ ∼ D / P • D These statements are:

If Fordham expands course offerings, then if Georgetown increases its endowment, then both Duke raises tuition and Tulane reduces class size.

(∼H ⊃ K) • (H ⊃ ∼T)

Progressive increases its territory if neither Safeco cuts costs nor Travelers runs an ad.

Either Breitling has a diamond model and Rado advertises a calendar watch or Tissot has luminous hands.

Proposition 1H Given the following proposition: [(A ≡ ∼B) ∨ (X ⊃ Y)] • [(Y ⊃ A) ≡ ∼(X ∨ B)] -In Proposition 1H, the main operator is a:

Not both Playboy changes its image and Maxim changes its cover given that Glamour hires models.

Given the argument: W ∨ ∼ S / E ∨ ∼ A / (K ∨ L) ≡ (A • S) // L ⊃ (E • W) This argument is:

∼Q ∨ S

∼N ∨ A

Given the argument: A ⊃ ∼B / B ∨ A // ∼B ≡ A. This argument is:

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

Given the pair of statements: ∼ (H ≡ R) and ∼ (R ⊃ ∼ H) These statements are:

Given the pair of statements: J ≡ ∼ M and (J • M) ∨ ∼(M ∨ J) These statements are:

Statement 2H Given the following statement: [N ∨ ∼ (K ∨ G)] ≡ [(G ⊃ N) • (K ⊃ N)] -Statement 2H is:

Given the statements: W ⊃ (E ∨ ∼ G) / A ⊃ (G ∨ ∼ E) / H ⊃ (A • W) / H • E These statements are:

Given the argument: K ⊃ (M ∨ ∼ H) / M ⊃ H / M ⊃ K // K ⊃ H 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