Question 1

(?H ? K) • (H ? ?T) $\frac{\mathrm{H} \vee \sim \mathrm{H}}{\sim \mathrm{T} \vee \mathrm{K}}$

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 2

Given the argument: M ⊃ Q / M ∨ ∼ Q // M • Q
This argument is:

Accepted Answer

A)  Invalid; fails in 4th line. 
B)  Valid. 
C)  Invalid; fails in 5th line. 
D)  Invalid; fails in 2nd line. 
E)  Invalid; fails in 3rd line. 
A)  Invalid; fails in 4th line. 
B)  Valid. 
C)  Invalid; fails in 5th line. 
D)  Invalid; fails in 2nd line. 
E)  Invalid; fails in 3rd line.

Question 3

Honda's reducing inventory is a sufficient and necessary condition for Toyota's closing a factory; also, Nissan lays off workers only if either Chrysler or Fiat does not improve mileage.

Accepted Answer

A)  (H ⊃ T) • [N ⊃ ∼(C ∨ F)] 
B)  H ≡ {T ⊃ [N ⊃ (∼C ∨ ∼F)]} 
C)  [H ≡ (T • N)] ⊃ (∼C ∨ ∼F) 
D)  (H ≡ T) • [(∼C ∨ ∼F) ⊃ N] 
E)  (H ≡ T) • [N ⊃ (∼C ∨ ∼F)] 
A)  (H ⊃ T) • [N ⊃ ∼(C ∨ F)] 
B)  H ≡ {T ⊃ [N ⊃ (∼C ∨ ∼F)]} 
C)  [H ≡ (T • N)] ⊃ (∼C ∨ ∼F) 
D)  (H ≡ T) • [(∼C ∨ ∼F) ⊃ N] 
E)  (H ≡ T) • [N ⊃ (∼C ∨ ∼F)]

Question 4

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

Accepted Answer

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

Question 5

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 6

?T ? F $\frac { \sim \mathrm { F } \supset \mathrm { G } } { \sim \mathrm { T } \supset \mathrm { G } }$

Accepted Answer

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

Question 7

If an ordinary truth table is constructed for a valid argument, then:

Accepted Answer

A)  There may be one line that has true premise(s) and false conclusion. 
B)  There is no line that has true premise(s) and false conclusion. 
C)  There must be at least one line that has true premise(s) and false conclusion. 
D)  There must be at least one line that has true premise(s) and true conclusion. 
E)  There must be exactly one line that has true premise(s) and true conclusion. 
A)  There may be one line that has true premise(s) and false conclusion. 
B)  There is no line that has true premise(s) and false conclusion. 
C)  There must be at least one line that has true premise(s) and false conclusion. 
D)  There must be at least one line that has true premise(s) and true conclusion. 
E)  There must be exactly one line that has true premise(s) and true conclusion.

Question 8

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

Accepted Answer

A) True 
 B)False

Question 9

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

Accepted Answer

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

Question 10

If Movado offers a blue dial, then neither Fossil is water resistant nor Nautica promotes a titanium case.

Accepted Answer

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

Question 11

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 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

D ? ?N $\frac { \sim \mathrm { N } } { \mathrm { D } }$

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 15

?B ? K $\frac { \sim \mathrm { W } \supset \sim \mathrm { B } } { \mathrm { W } \supset \sim \mathrm { K } }$

Accepted Answer

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

Question 16

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 17

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

Accepted Answer

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

Question 18

Metropolitan's reorganizing implies that Allstate hires agents, provided that Liberty reduces premiums.

Accepted Answer

A)  M ⊃ (L ⊃ 
A)  
B)  L ⊃ (A ⊃ M) 
C)  (L ⊃ M) ⊃ A 
D)  M ⊃ (A ⊃ L) 
E)  L ⊃ (M ⊃ 
A)  
A)  M ⊃ (L ⊃ 
A)  
B)  L ⊃ (A ⊃ M) 
C)  (L ⊃ M) ⊃ A 
D)  M ⊃ (A ⊃ L) 
E)  L ⊃ (M ⊃ 
A)

Question 19

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

Accepted Answer

A) True 
 B)False

Question 20

Given the pair of statements: A ∨ (B • C) and (B • ∼ A) ∨ (A • ∼ C).
These statements are:

Accepted Answer

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

(?H ? K) • (H ? ?T) $\frac{\mathrm{H} \vee \sim \mathrm{H}}{\sim \mathrm{T} \vee \mathrm{K}}$

Given the argument: M ⊃ Q / M ∨ ∼ Q // M • Q This argument is:

Honda's reducing inventory is a sufficient and necessary condition for Toyota's closing a factory; also, Nissan lays off workers only if either Chrysler or Fiat does not improve mileage.

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

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

?T ? F $\frac { \sim \mathrm { F } \supset \mathrm { G } } { \sim \mathrm { T } \supset \mathrm { G } }$

If an ordinary truth table is constructed for a valid argument, then:

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

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

If Movado offers a blue dial, then neither Fossil is water resistant nor Nautica promotes a titanium case.

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

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

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

D ? ?N $\frac { \sim \mathrm { N } } { \mathrm { D } }$

?B ? K $\frac { \sim \mathrm { W } \supset \sim \mathrm { B } } { \mathrm { W } \supset \sim \mathrm { K } }$

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

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

Metropolitan's reorganizing implies that Allstate hires agents, provided that Liberty reduces premiums.

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

Given the pair of statements: A ∨ (B • C) and (B • ∼ A) ∨ (A • ∼ C). These statements are:

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

(?H ? K) • (H ? ?T) H∨∼H∼T∨K\frac{\mathrm{H} \vee \sim \mathrm{H}}{\sim \mathrm{T} \vee \mathrm{K}}∼T∨KH∨∼H​

Given the argument: M ⊃ Q / M ∨ ∼ Q // M • Q This argument is:

Honda's reducing inventory is a sufficient and necessary condition for Toyota's closing a factory; also, Nissan lays off workers only if either Chrysler or Fiat does not improve mileage.

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

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

?T ? F ∼F⊃G∼T⊃G\frac { \sim \mathrm { F } \supset \mathrm { G } } { \sim \mathrm { T } \supset \mathrm { G } }∼T⊃G∼F⊃G​

If an ordinary truth table is constructed for a valid argument, then:

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

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

If Movado offers a blue dial, then neither Fossil is water resistant nor Nautica promotes a titanium case.

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

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

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

D ? ?N ∼ND\frac { \sim \mathrm { N } } { \mathrm { D } }D∼N​

?B ? K ∼W⊃∼BW⊃∼K\frac { \sim \mathrm { W } \supset \sim \mathrm { B } } { \mathrm { W } \supset \sim \mathrm { K } }W⊃∼K∼W⊃∼B​

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

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

Metropolitan's reorganizing implies that Allstate hires agents, provided that Liberty reduces premiums.

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

Given the pair of statements: A ∨ (B • C) and (B • ∼ A) ∨ (A • ∼ C). These statements are:

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

(?H ? K) • (H ? ?T) $\frac{\mathrm{H} \vee \sim \mathrm{H}}{\sim \mathrm{T} \vee \mathrm{K}}$

?T ? F $\frac { \sim \mathrm { F } \supset \mathrm { G } } { \sim \mathrm { T } \supset \mathrm { G } }$

D ? ?N $\frac { \sim \mathrm { N } } { \mathrm { D } }$

?B ? K $\frac { \sim \mathrm { W } \supset \sim \mathrm { B } } { \mathrm { W } \supset \sim \mathrm { K } }$