Question 1

Given the argument: H ⊃ (R • J) / (R ∨ A) ⊃ E / J ⊃ ∼ P / E ⊃ P // ∼ H
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 2

∼S ∨ ∼T

Accepted Answer

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

Question 3

Statement 3G
Given the following statement:
[A • (B ∨ C)] ∨ [∼ (A • B) ∨ ∼ (A • C)]
-The truth table for Statement 3G has how many lines?

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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 6

Norwegian improves its entertainment only if both Disney does not promote family cruises and Windstar does not diversify its activities.

Accepted Answer

A)  N ⊃ (∼D ∨ ∼W) 
B)  N ⊃ (∼D • ∼W) 
C)  (∼D • ∼W) ⊃ N 
D)  N ⊃ ∼(D • W) 
E)  ∼(D • W) ⊃ N 
A)  N ⊃ (∼D ∨ ∼W) 
B)  N ⊃ (∼D • ∼W) 
C)  (∼D • ∼W) ⊃ N 
D)  N ⊃ ∼(D • W) 
E)  ∼(D • W) ⊃ N

Question 7

L ∼N ⊃ L
∼N

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

(∼N ⊃ R) • (F ⊃ ∼G)

Accepted Answer

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

Question 10

Cosmo raises its price if and only if both Redbook increases circulation and Glamour hires new writers, but either Shape or Health expands coverage if Forbes adds new features.

Accepted Answer

A)  [(C ≡ R) • G] • [(F ⊃ S) ∨ H] 
B)  (R • G) ≡ [(C ⊃ F) ⊃ (S ∨ H)] 
C)  [C ≡ (R • G)] • [F ⊃ (S ∨ H)] 
D)  [C ⊃ (R • G)] • [F ≡ (S ∨ H)] 
E)  C ≡ {(R • G) • [F ⊃ (S ∨ H)]} 
A)  [(C ≡ R) • G] • [(F ⊃ S) ∨ H] 
B)  (R • G) ≡ [(C ⊃ F) ⊃ (S ∨ H)] 
C)  [C ≡ (R • G)] • [F ⊃ (S ∨ H)] 
D)  [C ⊃ (R • G)] • [F ≡ (S ∨ H)] 
E)  C ≡ {(R • G) • [F ⊃ (S ∨ H)]}

Question 11

Either taxes will be imposed on sugary drinks or public health will deteriorate. Therefore, public health will deteriorate, since taxes will not be imposed on sugary drinks.

Accepted Answer

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

Question 12

Given the pair of statements: M ⊃ L and ∼ (L ⊃ M)
These statements are:

Accepted Answer

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

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

∼G

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 15

Travelers and Farmers cut costs given that Safeco opens new offices, but Metropolitan restructures if and only if either Nationwide expands coverage or Conseco reduces premiums.

Accepted Answer

A)  [(T • F) ⊃ S] • [(N ∨ 
C)  ⊃ M] 
B)  [(T • F) ⊃ S] ⊃ [M ≡ (N ∨
C) ] 
C)  [(T • F) ⊃ S] • [M ≡ (N ∨ 
C) ] 
D)  [S ⊃ (T • F)] • [M ≡ (N ∨ 
C) ] 
E)  [S ⊃ (T • F)] • [M ⊃ (N ∨ 
C) ] 
A)  [(T • F) ⊃ S] • [(N ∨ 
C)  ⊃ M] 
B)  [(T • F) ⊃ S] ⊃ [M ≡ (N ∨
C) ] 
C)  [(T • F) ⊃ S] • [M ≡ (N ∨ 
C) ] 
D)  [S ⊃ (T • F)] • [M ≡ (N ∨ 
C) ] 
E)  [S ⊃ (T • F)] • [M ⊃ (N ∨ 
C) ]

Question 16

Forbes increases circulation if and only if both Shape and Health do not raise their price.

Accepted Answer

A)  F ≡ (∼S ∨ ∼H) 
B)  F ⊃ (∼S • ∼H) 
C)  F ≡ (∼S • ∼H) 
D)  F ≡ ∼(S • H) 
E)  (∼S • ∼H) ⊃ F 
A)  F ≡ (∼S ∨ ∼H) 
B)  F ⊃ (∼S • ∼H) 
C)  F ≡ (∼S • ∼H) 
D)  F ≡ ∼(S • H) 
E)  (∼S • ∼H) ⊃ F

Question 17

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

Accepted Answer

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

Question 18

United's lowering fares is a sufficient and necessary condition for American's hiring pilots, given that Frontier does not improve service.

Accepted Answer

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

Question 19

W

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 20

Budweiser is bland if either Heineken is balanced or Foster's is refreshing.

Accepted Answer

A)  (H ⊃ 
B)  ∨ F 
B)  (B ⊃ H) ∨ F 
C)  B ⊃ (H ∨ F) 
D)  B ⊃ H ∨ F 
E)  (H ∨ F) ⊃ B 
A)  (H ⊃ 
B)  ∨ F 
B)  (B ⊃ H) ∨ F 
C)  B ⊃ (H ∨ F) 
D)  B ⊃ H ∨ F 
E)  (H ∨ F) ⊃ B

Given the argument: H ⊃ (R • J) / (R ∨ A) ⊃ E / J ⊃ ∼ P / E ⊃ P // ∼ H This argument is:

∼S ∨ ∼T

Statement 3G Given the following statement: [A • (B ∨ C)] ∨ [∼ (A • B) ∨ ∼ (A • C)] -The truth table for Statement 3G has how many lines?

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

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.

Norwegian improves its entertainment only if both Disney does not promote family cruises and Windstar does not diversify its activities.

L ∼N ⊃ L ∼N

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

(∼N ⊃ R) • (F ⊃ ∼G)

Cosmo raises its price if and only if both Redbook increases circulation and Glamour hires new writers, but either Shape or Health expands coverage if Forbes adds new features.

Either taxes will be imposed on sugary drinks or public health will deteriorate. Therefore, public health will deteriorate, since taxes will not be imposed on sugary drinks.

Given the pair of statements: M ⊃ L and ∼ (L ⊃ M) These statements are:

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

∼G

Travelers and Farmers cut costs given that Safeco opens new offices, but Metropolitan restructures if and only if either Nationwide expands coverage or Conseco reduces premiums.

Forbes increases circulation if and only if both Shape and Health do not raise their price.

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

United's lowering fares is a sufficient and necessary condition for American's hiring pilots, given that Frontier does not improve service.

W

Budweiser is bland if either Heineken is balanced or Foster's is refreshing.

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 argument: H ⊃ (R • J) / (R ∨ A) ⊃ E / J ⊃ ∼ P / E ⊃ P // ∼ H This argument is:

∼S ∨ ∼T

Statement 3G Given the following statement: [A • (B ∨ C)] ∨ [∼ (A • B) ∨ ∼ (A • C)] -The truth table for Statement 3G has how many lines?

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

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.

Norwegian improves its entertainment only if both Disney does not promote family cruises and Windstar does not diversify its activities.

L ∼N ⊃ L ∼N

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

(∼N ⊃ R) • (F ⊃ ∼G)

Cosmo raises its price if and only if both Redbook increases circulation and Glamour hires new writers, but either Shape or Health expands coverage if Forbes adds new features.

Either taxes will be imposed on sugary drinks or public health will deteriorate. Therefore, public health will deteriorate, since taxes will not be imposed on sugary drinks.

Given the pair of statements: M ⊃ L and ∼ (L ⊃ M) These statements are:

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

∼G

Travelers and Farmers cut costs given that Safeco opens new offices, but Metropolitan restructures if and only if either Nationwide expands coverage or Conseco reduces premiums.

Forbes increases circulation if and only if both Shape and Health do not raise their price.

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

United's lowering fares is a sufficient and necessary condition for American's hiring pilots, given that Frontier does not improve service.

W

Budweiser is bland if either Heineken is balanced or Foster's is refreshing.

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