Question 1

Statement 3A
Given the following statement:
[∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)]
-The truth table for Statement 3A has how many lines?

Accepted Answer

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

Question 2

K ? R $\frac { E \supset R } { K \supset E }$

Accepted Answer

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

Question 3

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 4

?P ? M $\frac { \mathrm { P } } { \mathrm { M } }$

Accepted Answer

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

Question 5

(J ? ?M) • (?A ? R) $\frac { \mathrm { M } V \sim \mathrm { R } } { \sim \mathrm { J } \vee \mathrm { A } }$

Accepted Answer

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

Question 6

K ∨ ∼B B
K

Accepted Answer

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

Question 7

Given the pair of statements: N ∨ (E • ∼ H) and (H • ∼ N) ∨ ∼ (E ∨ N)
These statements are:

Accepted Answer

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

Question 8

If Heineken's being balanced implies that either Sierra is hearty or Alaskan is not sweet, then Miller's being zesty is a sufficient and necessary condition for Coors's being smooth.

Accepted Answer

A)  [H ⊃ ∼(S ∨ 
A) ] ⊃ (M ≡ 
C)  
B)  [H ⊃ (S ∨ ∼
A) ] ⊃ (M ≡ 
C)  
C)  [H ≡ (S ∨ ∼
A) ] ⊃ (M ⊃ 
C)  
D)  H ⊃ [(S ∨ ∼
A)  ≡ (M ⊃ 
C) ] 
E)  H ⊃ [(S ∨ ∼
A)  ⊃ (M ≡ 
C) ] 
A)  [H ⊃ ∼(S ∨ 
A) ] ⊃ (M ≡ 
C)  
B)  [H ⊃ (S ∨ ∼
A) ] ⊃ (M ≡ 
C)  
C)  [H ≡ (S ∨ ∼
A) ] ⊃ (M ⊃ 
C)  
D)  H ⊃ [(S ∨ ∼
A)  ≡ (M ⊃ 
C) ] 
E)  H ⊃ [(S ∨ ∼
A)  ⊃ (M ≡ 
C) ]

Question 9

Statement 1E
Given the following statement:
(G ≡ ∼ H) ∨ (H ⊃ G)
-The truth table for Statement 1E has how many lines?

Accepted Answer

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

Question 10

Statement 2B
Given the following statement:
[N ≡ (S • J)] ⊃ [S ⊃ (N ⊃ J)]
-The truth table for Statement 2B has how many lines?

Accepted Answer

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

Question 11

Statement 3D
Given the following statement:
(M ⊃ ∼ E) ∨ (R ⊃ E)
-The truth table for Statement 3D 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 12

Statement 1B
(R • B) ≡ (B ⊃ ∼ R)
-Statement 1B is:

Accepted Answer

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

Question 13

If computers can play chess, then they can think. But computers cannot think. Thus, computers cannot play chess.

Accepted Answer

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

Question 14

Statement 3I
Given the following statement:
[K • (P ∨ ∼ R)] • [K ⊃ (R • ∼ P)]
-The truth table for Statement 3I has how many lines?

Accepted Answer

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

Question 15

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 16

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

Accepted Answer

A) True 
 B)False

Question 17

?A ? ?H $\frac{\mathrm{E} \supset \sim \mathrm{A}}{\mathrm{E} \supset \sim \mathrm{H}}$

Accepted Answer

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

Question 18

Statement 2H
Given the following statement:
[N ∨ ∼ (K ∨ G)] ≡ [(G ⊃ N) • (K ⊃ N)]
-Statement 2H is:

Accepted Answer

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

Question 19

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 20

?A ? ?F $\underline { \mathrm { C } } \supset \sim \mathrm { A }$
$\overline { \mathrm { C } \supset \sim \mathrm { F } }$

Accepted Answer

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

Statement 3A Given the following statement: [∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)] -The truth table for Statement 3A has how many lines?

K ? R $\frac { E \supset R } { K \supset E }$

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

?P ? M $\frac { \mathrm { P } } { \mathrm { M } }$

(J ? ?M) • (?A ? R) $\frac { \mathrm { M } V \sim \mathrm { R } } { \sim \mathrm { J } \vee \mathrm { A } }$

K ∨ ∼B B K

Given the pair of statements: N ∨ (E • ∼ H) and (H • ∼ N) ∨ ∼ (E ∨ N) These statements are:

If Heineken's being balanced implies that either Sierra is hearty or Alaskan is not sweet, then Miller's being zesty is a sufficient and necessary condition for Coors's being smooth.

Statement 1E Given the following statement: (G ≡ ∼ H) ∨ (H ⊃ G) -The truth table for Statement 1E has how many lines?

Statement 2B Given the following statement: [N ≡ (S • J)] ⊃ [S ⊃ (N ⊃ J)] -The truth table for Statement 2B has how many lines?

Statement 3D Given the following statement: (M ⊃ ∼ E) ∨ (R ⊃ E) -The truth table for Statement 3D has how many lines?

Statement 1B (R • B) ≡ (B ⊃ ∼ R) -Statement 1B is:

If computers can play chess, then they can think. But computers cannot think. Thus, computers cannot play chess.

Statement 3I Given the following statement: [K • (P ∨ ∼ R)] • [K ⊃ (R • ∼ P)] -The truth table for Statement 3I has how many lines?

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.

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

?A ? ?H $\frac{\mathrm{E} \supset \sim \mathrm{A}}{\mathrm{E} \supset \sim \mathrm{H}}$

Statement 2H Given the following statement: [N ∨ ∼ (K ∨ G)] ≡ [(G ⊃ N) • (K ⊃ N)] -Statement 2H is:

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.

?A ? ?F $\underline { \mathrm { C } } \supset \sim \mathrm { A }$ $\overline { \mathrm { C } \supset \sim \mathrm { F } }$

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

Statement 3A Given the following statement: [∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)] -The truth table for Statement 3A has how many lines?

K ? R E⊃RK⊃E\frac { E \supset R } { K \supset E }K⊃EE⊃R​

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

?P ? M PM\frac { \mathrm { P } } { \mathrm { M } }MP​

(J ? ?M) • (?A ? R) MV∼R∼J∨A\frac { \mathrm { M } V \sim \mathrm { R } } { \sim \mathrm { J } \vee \mathrm { A } }∼J∨AMV∼R​

K ∨ ∼B B K

Given the pair of statements: N ∨ (E • ∼ H) and (H • ∼ N) ∨ ∼ (E ∨ N) These statements are:

If Heineken's being balanced implies that either Sierra is hearty or Alaskan is not sweet, then Miller's being zesty is a sufficient and necessary condition for Coors's being smooth.

Statement 1E Given the following statement: (G ≡ ∼ H) ∨ (H ⊃ G) -The truth table for Statement 1E has how many lines?

Statement 2B Given the following statement: [N ≡ (S • J)] ⊃ [S ⊃ (N ⊃ J)] -The truth table for Statement 2B has how many lines?

Statement 3D Given the following statement: (M ⊃ ∼ E) ∨ (R ⊃ E) -The truth table for Statement 3D has how many lines?

Statement 1B (R • B) ≡ (B ⊃ ∼ R) -Statement 1B is:

If computers can play chess, then they can think. But computers cannot think. Thus, computers cannot play chess.

Statement 3I Given the following statement: [K • (P ∨ ∼ R)] • [K ⊃ (R • ∼ P)] -The truth table for Statement 3I has how many lines?

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.

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

?A ? ?H E⊃∼AE⊃∼H\frac{\mathrm{E} \supset \sim \mathrm{A}}{\mathrm{E} \supset \sim \mathrm{H}}E⊃∼HE⊃∼A​

Statement 2H Given the following statement: [N ∨ ∼ (K ∨ G)] ≡ [(G ⊃ N) • (K ⊃ N)] -Statement 2H is:

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.

?A ? ?F C‾⊃∼A\underline { \mathrm { C } } \supset \sim \mathrm { A }C​⊃∼A C⊃∼F‾\overline { \mathrm { C } \supset \sim \mathrm { F } }C⊃∼F​

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

K ? R $\frac { E \supset R } { K \supset E }$

?P ? M $\frac { \mathrm { P } } { \mathrm { M } }$

(J ? ?M) • (?A ? R) $\frac { \mathrm { M } V \sim \mathrm { R } } { \sim \mathrm { J } \vee \mathrm { A } }$

?A ? ?H $\frac{\mathrm{E} \supset \sim \mathrm{A}}{\mathrm{E} \supset \sim \mathrm{H}}$

?A ? ?F $\underline { \mathrm { C } } \supset \sim \mathrm { A }$ $\overline { \mathrm { C } \supset \sim \mathrm { F } }$