Question 1

Toyota's closing a factory implies that Fiat improves mileage, given that both Chrysler and Nissan do not increase sales.

Accepted Answer

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

Question 2

Given the argument: K ⊃ Q / Q ⊃ ∼ K // K ≡ Q
This argument is:

Accepted Answer

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

Question 3

D ∨ M

Accepted Answer

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

Question 4

Statement 2C
Given the following statement:
[G ⊃ (R • N)] ∨ [R ⊃ (G • N)]
-The truth table for Statement 2C has how many lines?

Accepted Answer

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

Question 5

If eggs do not contain cholesterol, then they are healthy to eat. But eggs do contain cholesterol. Thus, eggs are not healthy to eat.

Accepted Answer

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

Question 6

Rice hires new faculty only if neither Duke nor Tulane increases student aid.

Accepted Answer

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

Question 7

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 8

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 9

Given the argument: S ⊃ E / N ⊃ (∼ S ⊃ E) // N ⊃ E
This argument is:

Accepted Answer

A)  Invalid; fails in 5th line. 
B)  Invalid; fails in 6th line. 
C)  Valid. 
D)  Invalid; fails in 2nd line. 
E)  Invalid; fails in 3rd line. 
A)  Invalid; fails in 5th line. 
B)  Invalid; fails in 6th line. 
C)  Valid. 
D)  Invalid; fails in 2nd line. 
E)  Invalid; fails in 3rd line.

Question 10

Princess drops its dress codes or Oceania enlarges its fleet, and Seabourn reduces its fares.

Accepted Answer

A)  P • (O ∨ S) 
B)  (P • O) ∨ S 
C)  P ∨ (O • S) 
D)  P ∨ O • S 
E)  (P ∨ O) • S 
A)  P • (O ∨ S) 
B)  (P • O) ∨ S 
C)  P ∨ (O • S) 
D)  P ∨ O • S 
E)  (P ∨ O) • S

Question 11

∼P ⊃ ∼D

Accepted Answer

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

Question 12

∼F ∼B ⊃ F
B

Accepted Answer

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

Question 13

Given the argument: G ⊃ (N • E) / H ⊃ N / K ⊃ ∼E / (H • K) ≡ G
This argument is:

Accepted Answer

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

Question 14

Given the statements: N ⊃ (L • S) / (S ∨ W) ⊃ B / G ⊃ ∼ B / G ⊃ N
These statements are:

Accepted Answer

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

Question 15

Statement 2D
Given the following statement:
[(N ∨ R) ⊃ ∼ R] ≡ R
-Statement 2D is:

Accepted Answer

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

Question 16

(K ⊃ ∼A) • (S ⊃ ∼D)

Accepted Answer

A)  Invalid. 
B)  Modus tollens. 
C)  Affirming the consequent. 
D)  Denying the antecedent. 
E)  Destructive dilemma. 
A)  Invalid. 
B)  Modus tollens. 
C)  Affirming the consequent. 
D)  Denying the antecedent. 
E)  Destructive dilemma.

Question 17

Given the statements: S ⊃ (Q ∨ L) / (Q ∨ G) ⊃ (S ⊃ N) / L ⊃ (N ∨ ∼ S) / S • ∼ N
These statements are:

Accepted Answer

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

Question 18

Given the argument: (A • B) ≡ (C ∨ D) / A ⊃ E / B ⊃ F // C ⊃ (E • F).
This argument is:

Accepted Answer

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

Question 19

Suppose an indirect truth table is constructed for a series of statements, and the truth table requires more than one line. If a contradiction is reached on the first line, then:

Accepted Answer

A)  The statements are consistent. 
B)  The statements are contingent. 
C)  The statements are inconsistent. 
D)  The statements could still be invalid. 
E)  The second line in the truth table must be completed. 
A)  The statements are consistent. 
B)  The statements are contingent. 
C)  The statements are inconsistent. 
D)  The statements could still be invalid. 
E)  The second line in the truth table must be completed.

Question 20

∼D ⊃ ∼C

Accepted Answer

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

Toyota's closing a factory implies that Fiat improves mileage, given that both Chrysler and Nissan do not increase sales.

Given the argument: K ⊃ Q / Q ⊃ ∼ K // K ≡ Q This argument is:

D ∨ M

Statement 2C Given the following statement: [G ⊃ (R • N)] ∨ [R ⊃ (G • N)] -The truth table for Statement 2C has how many lines?

If eggs do not contain cholesterol, then they are healthy to eat. But eggs do contain cholesterol. Thus, eggs are not healthy to eat.

Rice hires new faculty only if neither Duke nor Tulane increases student aid.

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.

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

Given the argument: S ⊃ E / N ⊃ (∼ S ⊃ E) // N ⊃ E This argument is:

Princess drops its dress codes or Oceania enlarges its fleet, and Seabourn reduces its fares.

∼P ⊃ ∼D

∼F ∼B ⊃ F B

Given the argument: G ⊃ (N • E) / H ⊃ N / K ⊃ ∼E / (H • K) ≡ G This argument is:

Given the statements: N ⊃ (L • S) / (S ∨ W) ⊃ B / G ⊃ ∼ B / G ⊃ N These statements are:

Statement 2D Given the following statement: [(N ∨ R) ⊃ ∼ R] ≡ R -Statement 2D is:

(K ⊃ ∼A) • (S ⊃ ∼D)

Given the statements: S ⊃ (Q ∨ L) / (Q ∨ G) ⊃ (S ⊃ N) / L ⊃ (N ∨ ∼ S) / S • ∼ N These statements are:

Given the argument: (A • B) ≡ (C ∨ D) / A ⊃ E / B ⊃ F // C ⊃ (E • F). This argument is:

Suppose an indirect truth table is constructed for a series of statements, and the truth table requires more than one line. If a contradiction is reached on the first line, then:

∼D ⊃ ∼C

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

Toyota's closing a factory implies that Fiat improves mileage, given that both Chrysler and Nissan do not increase sales.

Given the argument: K ⊃ Q / Q ⊃ ∼ K // K ≡ Q This argument is:

D ∨ M

Statement 2C Given the following statement: [G ⊃ (R • N)] ∨ [R ⊃ (G • N)] -The truth table for Statement 2C has how many lines?

If eggs do not contain cholesterol, then they are healthy to eat. But eggs do contain cholesterol. Thus, eggs are not healthy to eat.

Rice hires new faculty only if neither Duke nor Tulane increases student aid.

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.

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

Given the argument: S ⊃ E / N ⊃ (∼ S ⊃ E) // N ⊃ E This argument is:

Princess drops its dress codes or Oceania enlarges its fleet, and Seabourn reduces its fares.

∼P ⊃ ∼D

∼F ∼B ⊃ F B

Given the argument: G ⊃ (N • E) / H ⊃ N / K ⊃ ∼E / (H • K) ≡ G This argument is:

Given the statements: N ⊃ (L • S) / (S ∨ W) ⊃ B / G ⊃ ∼ B / G ⊃ N These statements are:

Statement 2D Given the following statement: [(N ∨ R) ⊃ ∼ R] ≡ R -Statement 2D is:

(K ⊃ ∼A) • (S ⊃ ∼D)

Given the statements: S ⊃ (Q ∨ L) / (Q ∨ G) ⊃ (S ⊃ N) / L ⊃ (N ∨ ∼ S) / S • ∼ N These statements are:

Given the argument: (A • B) ≡ (C ∨ D) / A ⊃ E / B ⊃ F // C ⊃ (E • F). This argument is:

Suppose an indirect truth table is constructed for a series of statements, and the truth table requires more than one line. If a contradiction is reached on the first line, then:

∼D ⊃ ∼C

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