Question 1

It is not the case that either Honda reduces inventory and Mercedes introduces a new model or Toyota closes a factory and Fiat improves mileage.

Accepted Answer

A)  ∼(H • M) ∨ ∼(T • F) 
B)  (∼H • ∼M) ∨ (∼T • ∼F) 
C)  ∼[(H • M) ∨ (T • F)] 
D)  ∼(H ∨ M) • ∼(T ∨ F) 
E)  ∼ [(H ∨ M) • (T ∨ F)] 
A)  ∼(H • M) ∨ ∼(T • F) 
B)  (∼H • ∼M) ∨ (∼T • ∼F) 
C)  ∼[(H • M) ∨ (T • F)] 
D)  ∼(H ∨ M) • ∼(T ∨ F) 
E)  ∼ [(H ∨ M) • (T ∨ F)]

Question 2

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 3

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

Accepted Answer

A) True 
 B)False

Question 4

Honda reduces inventory if and only if Mercedes does not introduce a new model, unless Toyota closes a factory.

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

If Redbook's hiring models implies that Cosmo changes its cover, then either Maxim becomes more risqué or Playboy deletes its centerfold.

Accepted Answer

A)  R ⊃ [C ⊃ (M ∨ P)] 
B)  (R ⊃ 
C)  ≡ (M ∨ P) 
C)  (C ⊃ R) ⊃ (M ∨ P) 
D)  (R ⊃ 
C)  ⊃ (M ∨ P) 
E)  (M ∨ P) ⊃ (R ⊃ 
C)  
A)  R ⊃ [C ⊃ (M ∨ P)] 
B)  (R ⊃ 
C)  ≡ (M ∨ P) 
C)  (C ⊃ R) ⊃ (M ∨ P) 
D)  (R ⊃ 
C)  ⊃ (M ∨ P) 
E)  (M ∨ P) ⊃ (R ⊃ 
C)

Question 7

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

Accepted Answer

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

Question 8

Rice's reducing class size is a sufficient and necessary condition for Baylor's hiring new faculty unless Amherst's raising tuition implies that either Georgetown or Fordham does not offer new scholarships.

Accepted Answer

A)  (R ≡ 
B)  ∨ [A ⊃ (∼G ∨ ∼F)] 
B)  (B ⊃ R) ∨ [A ⊃ ∼(G • F)] 
C)  (R ⊃ 
B)  ⊃ [A ⊃ (∼G ∨ ∼F)] 
D)  [A ⊃ (∼G ∨ ∼F)] ⊃ (R ≡ 
B)  
E)  (R ≡ 
B)  ∨ [A ⊃ ∼(G ∨ F)] 
A)  (R ≡ 
B)  ∨ [A ⊃ (∼G ∨ ∼F)] 
B)  (B ⊃ R) ∨ [A ⊃ ∼(G • F)] 
C)  (R ⊃ 
B)  ⊃ [A ⊃ (∼G ∨ ∼F)] 
D)  [A ⊃ (∼G ∨ ∼F)] ⊃ (R ≡ 
B)  
E)  (R ≡ 
B)  ∨ [A ⊃ ∼(G ∨ F)]

Question 9

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

Accepted Answer

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

Question 10

If Forbes increases circulation, then if both Health raises its price and Shape expands coverage, then Money solicits new advertisers.

Accepted Answer

A)  F ⊃ [(H • S) ⊃ M] 
B)  (H • S) ⊃ (F ⊃ M) 
C)  F ⊃ (H • S) ⊃ M 
D)  [F ⊃ (H • S)] ⊃ M 
E)  (F ⊃ H) • (S ⊃ M) 
A)  F ⊃ [(H • S) ⊃ M] 
B)  (H • S) ⊃ (F ⊃ M) 
C)  F ⊃ (H • S) ⊃ M 
D)  [F ⊃ (H • S)] ⊃ M 
E)  (F ⊃ H) • (S ⊃ M)

Question 11

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

Accepted Answer

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

Question 12

Given the argument: Q ∨ ∼ S / ∼(N • A) / S ∨ A / (P • N) ∨ (G • Q) // P • G
This argument is:

Accepted Answer

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

Question 13

?D ? ?C $\frac { \mathrm { R } \supset \sim \mathrm { D } } { \mathrm { R } \supset \sim \mathrm { C } }$

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.

Question 14

Hertz's running a sale and Budget's lowering rates are a necessary condition for either Avis's buying new cars or Thrifty's laying off workers.

Accepted Answer

A)  (A • T) ⊃ (H ∨ 
B)  
B)  (H • 
B)  ⊃ (A ∨ T) 
C)  (H • 
B)  ∨ (A ∨ T) 
D)  (A ∨ T) ⊃ (H • 
B)  
E)  (H • 
B)  ≡ (A ∨ T) 
A)  (A • T) ⊃ (H ∨ 
B)  
B)  (H • 
B)  ⊃ (A ∨ T) 
C)  (H • 
B)  ∨ (A ∨ T) 
D)  (A ∨ T) ⊃ (H • 
B)  
E)  (H • 
B)  ≡ (A ∨ T)

Question 15

Piaget has a gold watch only if both Seiko has leather bands and Breitling has a diamond model.

Accepted Answer

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

Question 16

Seabourn revises its menu given that Norwegian and Princess halt tipping, unless Oceania enlarges its fleet if and only if both Costa improves its gym facilities and Regent enlarges its casinos.

Accepted Answer

A)  [S ⊃ (N • P)] ∨ [O ≡ (C • R)] 
B)  [(N • P) ≡ S] ∨ [O ⊃ (C • R)] 
C)  [(N • P) ⊃ S] ∨ [O ≡ (C • R)] 
D)  [S ⊃ (N • P)] ⊃ [O ≡ (C • R)] 
E)  [S ⊃ (N • P)] ≡ [O ∨ (C • R)] 
A)  [S ⊃ (N • P)] ∨ [O ≡ (C • R)] 
B)  [(N • P) ≡ S] ∨ [O ⊃ (C • R)] 
C)  [(N • P) ⊃ S] ∨ [O ≡ (C • R)] 
D)  [S ⊃ (N • P)] ⊃ [O ≡ (C • R)] 
E)  [S ⊃ (N • P)] ≡ [O ∨ (C • R)]

Question 17

Given the argument: R ⊃ (H • ∼N) / (H • ∼B) ⊃ (N ∨ ∼P) / K ⊃ (G • P) // (K • R) ⊃ B
This argument is:

Accepted Answer

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

Question 18

Given the argument: (S ∨ B) ⊃ M / S ∨ ∼ Q / A ⊃ B / A ∨ Q // M
This argument is:

Accepted Answer

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

Question 19

?G $\frac { \sim \mathrm { G } \supset \mathrm { A } } { \mathrm { A } }$

Accepted Answer

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

Question 20

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

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.

It is not the case that either Honda reduces inventory and Mercedes introduces a new model or Toyota closes a factory and Fiat improves mileage.

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

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

Honda reduces inventory if and only if Mercedes does not introduce a new model, unless Toyota closes a factory.

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

If Redbook's hiring models implies that Cosmo changes its cover, then either Maxim becomes more risqué or Playboy deletes its centerfold.

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

Rice's reducing class size is a sufficient and necessary condition for Baylor's hiring new faculty unless Amherst's raising tuition implies that either Georgetown or Fordham does not offer new scholarships.

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

If Forbes increases circulation, then if both Health raises its price and Shape expands coverage, then Money solicits new advertisers.

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

Given the argument: Q ∨ ∼ S / ∼(N • A) / S ∨ A / (P • N) ∨ (G • Q) // P • G This argument is:

?D ? ?C $\frac { \mathrm { R } \supset \sim \mathrm { D } } { \mathrm { R } \supset \sim \mathrm { C } }$

Hertz's running a sale and Budget's lowering rates are a necessary condition for either Avis's buying new cars or Thrifty's laying off workers.

Piaget has a gold watch only if both Seiko has leather bands and Breitling has a diamond model.

Seabourn revises its menu given that Norwegian and Princess halt tipping, unless Oceania enlarges its fleet if and only if both Costa improves its gym facilities and Regent enlarges its casinos.

Given the argument: R ⊃ (H • ∼N) / (H • ∼B) ⊃ (N ∨ ∼P) / K ⊃ (G • P) // (K • R) ⊃ B This argument is:

Given the argument: (S ∨ B) ⊃ M / S ∨ ∼ Q / A ⊃ B / A ∨ Q // M This argument is:

?G $\frac { \sim \mathrm { G } \supset \mathrm { A } } { \mathrm { A } }$

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

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

It is not the case that either Honda reduces inventory and Mercedes introduces a new model or Toyota closes a factory and Fiat improves mileage.

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

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

Honda reduces inventory if and only if Mercedes does not introduce a new model, unless Toyota closes a factory.

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

If Redbook's hiring models implies that Cosmo changes its cover, then either Maxim becomes more risqué or Playboy deletes its centerfold.

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

Rice's reducing class size is a sufficient and necessary condition for Baylor's hiring new faculty unless Amherst's raising tuition implies that either Georgetown or Fordham does not offer new scholarships.

D ? ?E ∼ED\frac { \sim \mathrm { E } } { \mathrm { D } }D∼E​

If Forbes increases circulation, then if both Health raises its price and Shape expands coverage, then Money solicits new advertisers.

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

Given the argument: Q ∨ ∼ S / ∼(N • A) / S ∨ A / (P • N) ∨ (G • Q) // P • G This argument is:

?D ? ?C R⊃∼DR⊃∼C\frac { \mathrm { R } \supset \sim \mathrm { D } } { \mathrm { R } \supset \sim \mathrm { C } }R⊃∼CR⊃∼D​

Hertz's running a sale and Budget's lowering rates are a necessary condition for either Avis's buying new cars or Thrifty's laying off workers.

Piaget has a gold watch only if both Seiko has leather bands and Breitling has a diamond model.

Seabourn revises its menu given that Norwegian and Princess halt tipping, unless Oceania enlarges its fleet if and only if both Costa improves its gym facilities and Regent enlarges its casinos.

Given the argument: R ⊃ (H • ∼N) / (H • ∼B) ⊃ (N ∨ ∼P) / K ⊃ (G • P) // (K • R) ⊃ B This argument is:

Given the argument: (S ∨ B) ⊃ M / S ∨ ∼ Q / A ⊃ B / A ∨ Q // M This argument is:

?G ∼G⊃AA\frac { \sim \mathrm { G } \supset \mathrm { A } } { \mathrm { A } }A∼G⊃A​

?K ? ?N ∼K∼N\frac { \sim \mathrm { K } } { \sim \mathrm { N } }∼N∼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

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

?D ? ?C $\frac { \mathrm { R } \supset \sim \mathrm { D } } { \mathrm { R } \supset \sim \mathrm { C } }$

?G $\frac { \sim \mathrm { G } \supset \mathrm { A } } { \mathrm { A } }$

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