Question 1

Given the pair of statements: ∼ (S ⊃ Q) and ∼ Q • S
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.

Question 2

Redbook's increasing its price is a sufficient and necessary condition for People's hiring new writers, provided that Health's expanding coverage implies that Shape changes its cover.

Accepted Answer

A)  R ≡ [P ⊃ (H ⊃S)] 
B)  (H ⊃ S) ⊃ (R ≡ P) 
C)  (R ≡ P) ⊃ (H ⊃ S) 
D)  (H ⊃ S) ⊃ (R ⊃ P)] 
E)  R ≡ [(H ⊃ S) ⊃ P] 
A)  R ≡ [P ⊃ (H ⊃S)] 
B)  (H ⊃ S) ⊃ (R ≡ P) 
C)  (R ≡ P) ⊃ (H ⊃ S) 
D)  (H ⊃ S) ⊃ (R ⊃ P)] 
E)  R ≡ [(H ⊃ S) ⊃ P]

Question 3

∼K ⊃ ∼N

Accepted Answer

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

Question 4

Redbook increases circulation or both Glamour hires models and Cosmo raises its price.

Accepted Answer

A)  R ∨ G • C 
B)  R ⊃ (G • 
C)  
C)  R • (G ∨ 
C)  
D)  (G • 
C)  ⊃ R 
E)  R ∨ (G • 
C)  
A)  R ∨ G • C 
B)  R ⊃ (G • 
C)  
C)  R • (G ∨ 
C)  
D)  (G • 
C)  ⊃ R 
E)  R ∨ (G • 
C)

Question 5

Given the statements: P ≡ (S ∨ ∼ A) / A ⊃ (M • J) / J ⊃ (P • S) / J ≡ A
These statements are:

Accepted Answer

A)  Valid. 
B)  Contradictory. 
C)  Tautologous. 
D)  Inconsistent. 
E)  Consistent. 
A)  Valid. 
B)  Contradictory. 
C)  Tautologous. 
D)  Inconsistent. 
E)  Consistent.

Question 6

Thrifty's laying off workers is a sufficient condition for National's improving efficiency, if Enterprise reorganizes.

Accepted Answer

A)  E ⊃ (N ⊃ T) 
B)  (T ⊃ N) ⊃ E 
C)  E ⊃ (T ⊃ N) 
D)  T ⊃ (N ⊃ 
E)  
E)  E ≡ (T ⊃ N) 
A)  E ⊃ (N ⊃ T) 
B)  (T ⊃ N) ⊃ E 
C)  E ⊃ (T ⊃ N) 
D)  T ⊃ (N ⊃ 
E)  
E)  E ≡ (T ⊃ N)

Question 7

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

Accepted Answer

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

Question 8

Given the statements: C ⊃ L / K ⊃ ∼H / L ⊃ (N ⊃ K) / C ⊃ (H ⊃ N) / C • H
These statements are:

Accepted Answer

A)  Contradictory. 
B)  Tautologous. 
C)  Consistent. 
D)  Inconsistent. 
E)  Valid. 
A)  Contradictory. 
B)  Tautologous. 
C)  Consistent. 
D)  Inconsistent. 
E)  Valid.

Question 9

JetBlue buys planes unless neither Frontier improves service nor United lowers fares.

Accepted Answer

A)  J ∨ ∼(F • U) 
B)  J ∨ ∼(F ∨ U) 
C)  J ∨ (∼F ∨ ∼U) 
D)  J ⊃ ∼(F ∨ U) 
E)  ∼(F ∨ U) ⊃ J 
A)  J ∨ ∼(F • U) 
B)  J ∨ ∼(F ∨ U) 
C)  J ∨ (∼F ∨ ∼U) 
D)  J ⊃ ∼(F ∨ U) 
E)  ∼(F ∨ U) ⊃ J

Question 10

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

Accepted Answer

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

Question 11

∼B ⊃ 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 12

G ∨ ∼T

Accepted Answer

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

Question 13

If deficit spending is halted, then interest rates will drop; but if inflation heats up, then interest rates will not drop. Accordingly, either deficit spending will not be halted or inflation will not heat up, since interest rates will either drop or not drop.

Accepted Answer

A)  Destructive dilemma. 
B)  Pure hypothetical syllogism. 
C)  Constructive dilemma. 
D)  Denying the antecedent. 
E)  Invalid. 
A)  Destructive dilemma. 
B)  Pure hypothetical syllogism. 
C)  Constructive dilemma. 
D)  Denying the antecedent. 
E)  Invalid.

Question 14

The truth table for Statement 1I 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.

Given the pair of statements: ∼ (S ⊃ Q) and ∼ Q • S These statements are:

Redbook's increasing its price is a sufficient and necessary condition for People's hiring new writers, provided that Health's expanding coverage implies that Shape changes its cover.

∼K ⊃ ∼N

Redbook increases circulation or both Glamour hires models and Cosmo raises its price.

Given the statements: P ≡ (S ∨ ∼ A) / A ⊃ (M • J) / J ⊃ (P • S) / J ≡ A These statements are:

Thrifty's laying off workers is a sufficient condition for National's improving efficiency, if Enterprise reorganizes.

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

Given the statements: C ⊃ L / K ⊃ ∼H / L ⊃ (N ⊃ K) / C ⊃ (H ⊃ N) / C • H These statements are:

JetBlue buys planes unless neither Frontier improves service nor United lowers fares.

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

∼B ⊃ K

G ∨ ∼T

If deficit spending is halted, then interest rates will drop; but if inflation heats up, then interest rates will not drop. Accordingly, either deficit spending will not be halted or inflation will not heat up, since interest rates will either drop or not drop.

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

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 pair of statements: ∼ (S ⊃ Q) and ∼ Q • S These statements are:

Redbook's increasing its price is a sufficient and necessary condition for People's hiring new writers, provided that Health's expanding coverage implies that Shape changes its cover.

∼K ⊃ ∼N

Redbook increases circulation or both Glamour hires models and Cosmo raises its price.

Given the statements: P ≡ (S ∨ ∼ A) / A ⊃ (M • J) / J ⊃ (P • S) / J ≡ A These statements are:

Thrifty's laying off workers is a sufficient condition for National's improving efficiency, if Enterprise reorganizes.

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

Given the statements: C ⊃ L / K ⊃ ∼H / L ⊃ (N ⊃ K) / C ⊃ (H ⊃ N) / C • H These statements are:

JetBlue buys planes unless neither Frontier improves service nor United lowers fares.

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

∼B ⊃ K

G ∨ ∼T

If deficit spending is halted, then interest rates will drop; but if inflation heats up, then interest rates will not drop. Accordingly, either deficit spending will not be halted or inflation will not heat up, since interest rates will either drop or not drop.

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

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