Question 1

Carnival advertises its parties if and only if Disney's promoting family cruises implies that Norwegian improves its entertainment.

Accepted Answer

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

Question 2

Either Chrysler's increasing sales is a necessary condition for Toyota's closing a factory or Nissan's laying off workers is a sufficient condition for Honda's reducing inventory.

Accepted Answer

A)  T ⊃ [C ⊃ (N ⊃ H)] 
B)  (C ⊃ T) ∨ (N ⊃ H) 
C)  (T ⊃ 
C)  ∨ (N ⊃ H) 
D)  T ⊃ [C ∨ (N ⊃ H)] 
E)  (C ⊃ T) ∨ (H ⊃ N) 
A)  T ⊃ [C ⊃ (N ⊃ H)] 
B)  (C ⊃ T) ∨ (N ⊃ H) 
C)  (T ⊃ 
C)  ∨ (N ⊃ H) 
D)  T ⊃ [C ∨ (N ⊃ H)] 
E)  (C ⊃ T) ∨ (H ⊃ N) C

Question 3

Statement 2A
Given the following statement:
(G ⊃ ∼ Q) ≡ ∼(Q • G)
-Statement 2A 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. C

Question 4

Given the pair of statements: (A ∨ B) • (∼ A ∨ ∼ B) and (B • A) ∨ (∼ A • ∼ B).
These statements are:

Accepted Answer

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

Question 5

Statement 2G
Given the following statement:
∼ (B ∨ A) ≡ (∼ A ⊃ B)
-Statement 2G is:

Accepted Answer

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

Question 6

National does not improve efficiency or Enterprise does not reorganize, given that Thrifty lays off workers.

Accepted Answer

A)  T ⊃ ∼(N ∨ 
E)  
B)  (∼N ∨ ∼
E)  ⊃ T 
C)  ∼(N ∨ 
E)  ⊃ T 
D)  (T ⊃ ∼N) ∨ ∼E 
E)  T ⊃ (∼N ∨ ∼
E)  
A)  T ⊃ ∼(N ∨ 
E)  
B)  (∼N ∨ ∼
E)  ⊃ T 
C)  ∼(N ∨ 
E)  ⊃ T 
D)  (T ⊃ ∼N) ∨ ∼E 
E)  T ⊃ (∼N ∨ ∼
E)

Question 7

Michelob's being complex is a necessary condition for Heineken's being balanced unless Alaskan's being sweet is a sufficient condition for Carlsberg's being malty.

Accepted Answer

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

Question 8

JetBlue buys planes if Delta advertises a sale, and Frontier improves service only if Southwest expands routes.

Accepted Answer

A)  (D ⊃ J) • (F ⊃ S) 
B)  (D ≡ J) • (F ≡ S) 
C)  (J ⊃ 
D)  • (S ⊃ F) 
D)  (D • J) ⊃ (S • F) 
E)  (J ⊃ 
D)  • (F ⊃ S) 
A)  (D ⊃ J) • (F ⊃ S) 
B)  (D ≡ J) • (F ≡ S) 
C)  (J ⊃ 
D)  • (S ⊃ F) 
D)  (D • J) ⊃ (S • F) 
E)  (J ⊃ 
D)  • (F ⊃ S)

Question 9

(?G ? E) • (R ? M) $\frac{R \vee \sim \mathrm{G}}{\mathrm{E} \vee \mathrm{M}}$

Accepted Answer

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

Question 10

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

Accepted Answer

A) True 
 B)False

Question 11

(L ? ?C) • (D ? ?Q) $\frac { \sim \mathrm { L } \vee \sim \mathrm { D } } { \mathrm { C } \vee \mathrm { Q } }$

Accepted Answer

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

Question 12

Statement 1I
Given the following statement:
(G • ∼ M) ⊃ (M ∨ G)
-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.

Question 13

Given the statements: A ≡ (B ∨C) / B ⊃ D / D ⊃ E / E ⊃ ∼ B / A ≡ ∼ C.
These statements are:

Accepted Answer

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

Question 14

Thrifty lays off workers only if neither National improves efficiency nor Enterprise reorganizes.

Accepted Answer

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

Question 15

Given the statements: R ⊃ (G ∨ Q) / G ⊃ (H • P) / Q ⊃ H / R ⊃ ∼ H
These statements are:

Accepted Answer

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

Question 16

Princess and Azmara improve gym facilities only if neither Carnival controls rowdiness nor Seabourn reduces fares.

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

?Q ? S $\frac { \sim \mathrm { Q } } { \mathrm { S } }$

Accepted Answer

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

Question 19

?N ? H $\mathrm { H }$
$\sim N$

Accepted Answer

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

Question 20

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.

Carnival advertises its parties if and only if Disney's promoting family cruises implies that Norwegian improves its entertainment.

Either Chrysler's increasing sales is a necessary condition for Toyota's closing a factory or Nissan's laying off workers is a sufficient condition for Honda's reducing inventory.

Statement 2A Given the following statement: (G ⊃ ∼ Q) ≡ ∼(Q • G) -Statement 2A is:

Given the pair of statements: (A ∨ B) • (∼ A ∨ ∼ B) and (B • A) ∨ (∼ A • ∼ B). These statements are:

Statement 2G Given the following statement: ∼ (B ∨ A) ≡ (∼ A ⊃ B) -Statement 2G is:

National does not improve efficiency or Enterprise does not reorganize, given that Thrifty lays off workers.

Michelob's being complex is a necessary condition for Heineken's being balanced unless Alaskan's being sweet is a sufficient condition for Carlsberg's being malty.

JetBlue buys planes if Delta advertises a sale, and Frontier improves service only if Southwest expands routes.

(?G ? E) • (R ? M) $\frac{R \vee \sim \mathrm{G}}{\mathrm{E} \vee \mathrm{M}}$

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

(L ? ?C) • (D ? ?Q) $\frac { \sim \mathrm { L } \vee \sim \mathrm { D } } { \mathrm { C } \vee \mathrm { Q } }$

Statement 1I Given the following statement: (G • ∼ M) ⊃ (M ∨ G) -The truth table for Statement 1I has how many lines?

Given the statements: A ≡ (B ∨C) / B ⊃ D / D ⊃ E / E ⊃ ∼ B / A ≡ ∼ C. These statements are:

Thrifty lays off workers only if neither National improves efficiency nor Enterprise reorganizes.

Given the statements: R ⊃ (G ∨ Q) / G ⊃ (H • P) / Q ⊃ H / R ⊃ ∼ H These statements are:

Princess and Azmara improve gym facilities only if neither Carnival controls rowdiness nor Seabourn reduces fares.

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

?Q ? S $\frac { \sim \mathrm { Q } } { \mathrm { S } }$

?N ? H $\mathrm { H }$ $\sim N$

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

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

Carnival advertises its parties if and only if Disney's promoting family cruises implies that Norwegian improves its entertainment.

Either Chrysler's increasing sales is a necessary condition for Toyota's closing a factory or Nissan's laying off workers is a sufficient condition for Honda's reducing inventory.

Statement 2A Given the following statement: (G ⊃ ∼ Q) ≡ ∼(Q • G) -Statement 2A is:

Given the pair of statements: (A ∨ B) • (∼ A ∨ ∼ B) and (B • A) ∨ (∼ A • ∼ B). These statements are:

Statement 2G Given the following statement: ∼ (B ∨ A) ≡ (∼ A ⊃ B) -Statement 2G is:

National does not improve efficiency or Enterprise does not reorganize, given that Thrifty lays off workers.

Michelob's being complex is a necessary condition for Heineken's being balanced unless Alaskan's being sweet is a sufficient condition for Carlsberg's being malty.

JetBlue buys planes if Delta advertises a sale, and Frontier improves service only if Southwest expands routes.

(?G ? E) • (R ? M) R∨∼GE∨M\frac{R \vee \sim \mathrm{G}}{\mathrm{E} \vee \mathrm{M}}E∨MR∨∼G​

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

(L ? ?C) • (D ? ?Q) ∼L∨∼DC∨Q\frac { \sim \mathrm { L } \vee \sim \mathrm { D } } { \mathrm { C } \vee \mathrm { Q } }C∨Q∼L∨∼D​

Statement 1I Given the following statement: (G • ∼ M) ⊃ (M ∨ G) -The truth table for Statement 1I has how many lines?

Given the statements: A ≡ (B ∨C) / B ⊃ D / D ⊃ E / E ⊃ ∼ B / A ≡ ∼ C. These statements are:

Thrifty lays off workers only if neither National improves efficiency nor Enterprise reorganizes.

Given the statements: R ⊃ (G ∨ Q) / G ⊃ (H • P) / Q ⊃ H / R ⊃ ∼ H These statements are:

Princess and Azmara improve gym facilities only if neither Carnival controls rowdiness nor Seabourn reduces fares.

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

?Q ? S ∼QS\frac { \sim \mathrm { Q } } { \mathrm { S } }S∼Q​

?N ? H H\mathrm { H }H ∼N\sim N∼N

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

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

(?G ? E) • (R ? M) $\frac{R \vee \sim \mathrm{G}}{\mathrm{E} \vee \mathrm{M}}$

(L ? ?C) • (D ? ?Q) $\frac { \sim \mathrm { L } \vee \sim \mathrm { D } } { \mathrm { C } \vee \mathrm { Q } }$

?Q ? S $\frac { \sim \mathrm { Q } } { \mathrm { S } }$

?N ? H $\mathrm { H }$ $\sim N$