Question 1

Statement 1H
Given the following statement:
(S ⊃ ∼ R) ⊃ (∼ S • R)
-The truth table for Statement 1H has how many lines?

Accepted Answer

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

Question 2

Given the statement: ∼ (S • ∼ D) ∨ (D ⊃ S)
This statement is:

Accepted Answer

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

Question 3

Statement 3G
Given the following statement:
[A • (B ∨ C)] ∨ [∼ (A • B) ∨ ∼ (A • C)]
-Statement 3G 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 4

S ? ?R $\frac { \mathrm { N } \supset \sim \mathrm { R } } { \mathrm { S } \supset \mathrm { N } }$

Accepted Answer

A)  Disjunctive syllogism. 
B)  Constructive dilemma. 
C)  Pure hypothetical syllogism. 
D)  Affirming the consequent. 
E)  Invalid. 
A)  Disjunctive syllogism. 
B)  Constructive dilemma. 
C)  Pure hypothetical syllogism. 
D)  Affirming the consequent. 
E)  Invalid.

Question 5

(R ? ?T) • (D ? T) $\frac { \sim \mathrm { T } \vee \mathrm { T } } { \sim \mathrm { R } \vee \sim \mathrm { D } }$

Accepted Answer

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

Question 6

If Chrysler increases sales, then it is not the case that both Mercedes introduces a new model and Nissan lays off workers.

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Given the argument: K ∨ B / K ≡ (D ∨ ∼ B) // K ⊃ D
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.

Question 9

Given the argument: R ∨ I / ∼ S ∨ (R ⊃ I) // S ⊃ I
This argument is:

Accepted Answer

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

Question 10

(B ? ?T) • (?B ? N) $\frac { \sim \mathrm { B } \vee \mathrm { B } } { \hline \mathrm { T } \vee \mathrm { N } }$

Accepted Answer

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

Question 11

Hertz runs a sale or both Avis buys new cars and Budget lowers rates.

Accepted Answer

A)  H ∨ A • B 
B)  H ∨ (A • 
B)  
C)  (H ∨ 
A)  • B 
D)  H • (A ∨ 
B)  
E)  H • A ∨ B 
A)  H ∨ A • B 
B)  H ∨ (A • 
B)  
C)  (H ∨ 
A)  • B 
D)  H • (A ∨ 
B)  
E)  H • A ∨ B

Question 12

Statement 1D
Given the following statement:
∼ (H ⊃ A) ∨ (A ⊃ H)
-Statement 1D is:

Accepted Answer

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

Question 13

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 14

?H ? ?B $\frac{\mathrm{B}}{\mathrm{H}}$

Accepted Answer

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

Question 15

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 16

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

Accepted Answer

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

Question 17

If dinosaur DNA has deteriorated, then it is impossible to recreate dinosaurs. If dinosaurs perished long ago, then dinosaur DNA has deteriorated. Hence, if dinosaurs perished long ago, then it is impossible to recreate them.

Accepted Answer

A)  Constructive dilemma. 
B)  Affirming the consequent. 
C)  Pure hypothetical syllogism. 
D)  Modus tollens. 
E)  Invalid. 
A)  Constructive dilemma. 
B)  Affirming the consequent. 
C)  Pure hypothetical syllogism. 
D)  Modus tollens. 
E)  Invalid.

Question 18

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 19

If an indirect truth table requiring more than one line is constructed for either an argument or a series of statements and no contradiction is derived on the first line, then:

Accepted Answer

A)  The argument is valid and the statements are consistent. 
B)  The argument is invalid and the statements are consistent. 
C)  The argument is valid and the statements are inconsistent. 
D)  The argument is invalid and the statements are inconsistent. 
E)  The second line of the truth table must be completed. 
A)  The argument is valid and the statements are consistent. 
B)  The argument is invalid and the statements are consistent. 
C)  The argument is valid and the statements are inconsistent. 
D)  The argument is invalid and the statements are inconsistent. 
E)  The second line of the truth table must be completed.

Question 20

K $\frac { \mathrm { G } \supset \sim \mathrm { K } } { \sim \mathrm { G } }$

Accepted Answer

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

Statement 1H Given the following statement: (S ⊃ ∼ R) ⊃ (∼ S • R) -The truth table for Statement 1H has how many lines?

Given the statement: ∼ (S • ∼ D) ∨ (D ⊃ S) This statement is:

Statement 3G Given the following statement: [A • (B ∨ C)] ∨ [∼ (A • B) ∨ ∼ (A • C)] -Statement 3G is:

S ? ?R $\frac { \mathrm { N } \supset \sim \mathrm { R } } { \mathrm { S } \supset \mathrm { N } }$

(R ? ?T) • (D ? T) $\frac { \sim \mathrm { T } \vee \mathrm { T } } { \sim \mathrm { R } \vee \sim \mathrm { D } }$

If Chrysler increases sales, then it is not the case that both Mercedes introduces a new model and Nissan lays off workers.

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

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

Given the argument: R ∨ I / ∼ S ∨ (R ⊃ I) // S ⊃ I This argument is:

(B ? ?T) • (?B ? N) $\frac { \sim \mathrm { B } \vee \mathrm { B } } { \hline \mathrm { T } \vee \mathrm { N } }$

Hertz runs a sale or both Avis buys new cars and Budget lowers rates.

Statement 1D Given the following statement: ∼ (H ⊃ A) ∨ (A ⊃ H) -Statement 1D is:

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

?H ? ?B $\frac{\mathrm{B}}{\mathrm{H}}$

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

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

If dinosaur DNA has deteriorated, then it is impossible to recreate dinosaurs. If dinosaurs perished long ago, then dinosaur DNA has deteriorated. Hence, if dinosaurs perished long ago, then it is impossible to recreate them.

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.

If an indirect truth table requiring more than one line is constructed for either an argument or a series of statements and no contradiction is derived on the first line, then:

K $\frac { \mathrm { G } \supset \sim \mathrm { K } } { \sim \mathrm { G } }$

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 1H Given the following statement: (S ⊃ ∼ R) ⊃ (∼ S • R) -The truth table for Statement 1H has how many lines?

Given the statement: ∼ (S • ∼ D) ∨ (D ⊃ S) This statement is:

Statement 3G Given the following statement: [A • (B ∨ C)] ∨ [∼ (A • B) ∨ ∼ (A • C)] -Statement 3G is:

S ? ?R N⊃∼RS⊃N\frac { \mathrm { N } \supset \sim \mathrm { R } } { \mathrm { S } \supset \mathrm { N } }S⊃NN⊃∼R​

(R ? ?T) • (D ? T) ∼T∨T∼R∨∼D\frac { \sim \mathrm { T } \vee \mathrm { T } } { \sim \mathrm { R } \vee \sim \mathrm { D } }∼R∨∼D∼T∨T​

If Chrysler increases sales, then it is not the case that both Mercedes introduces a new model and Nissan lays off workers.

P ? ?D ∼P∼D\frac { \sim \mathrm { P } } { \sim \mathrm { D } }∼D∼P​

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

Given the argument: R ∨ I / ∼ S ∨ (R ⊃ I) // S ⊃ I This argument is:

(B ? ?T) • (?B ? N) \frac { \sim \mathrm { B } \vee \mathrm { B } } { \hline \mathrm { T } \vee \mathrm { N } }

Hertz runs a sale or both Avis buys new cars and Budget lowers rates.

Statement 1D Given the following statement: ∼ (H ⊃ A) ∨ (A ⊃ H) -Statement 1D is:

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

?H ? ?B BH\frac{\mathrm{B}}{\mathrm{H}}HB​

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

W ∼W⊃∼KK\frac{\sim \mathrm{W} \supset \sim \mathrm{K}}{\mathrm{K}}K∼W⊃∼K​

If dinosaur DNA has deteriorated, then it is impossible to recreate dinosaurs. If dinosaurs perished long ago, then dinosaur DNA has deteriorated. Hence, if dinosaurs perished long ago, then it is impossible to recreate them.

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.

If an indirect truth table requiring more than one line is constructed for either an argument or a series of statements and no contradiction is derived on the first line, then:

K G⊃∼K∼G\frac { \mathrm { G } \supset \sim \mathrm { K } } { \sim \mathrm { G } }∼GG⊃∼K​

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

S ? ?R $\frac { \mathrm { N } \supset \sim \mathrm { R } } { \mathrm { S } \supset \mathrm { N } }$

(R ? ?T) • (D ? T) $\frac { \sim \mathrm { T } \vee \mathrm { T } } { \sim \mathrm { R } \vee \sim \mathrm { D } }$

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

(B ? ?T) • (?B ? N) $\frac { \sim \mathrm { B } \vee \mathrm { B } } { \hline \mathrm { T } \vee \mathrm { N } }$

?H ? ?B $\frac{\mathrm{B}}{\mathrm{H}}$

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

K $\frac { \mathrm { G } \supset \sim \mathrm { K } } { \sim \mathrm { G } }$