Question 1

Statement 3D
Given the following statement:
(M ⊃ ∼ E) ∨ (R ⊃ E)
-Statement 3D is:

Accepted Answer

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

Question 2

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) ]

Question 3

If Williams increases enrollment, then not both Fordham and Georgetown expand course offerings.

Accepted Answer

A)  W ∨ ∼(F ⊃ G) 
B)  W ⊃ ∼(F ∨ G) 
C)  W ⊃ (∼F • ∼G) 
D)  W ≡ ∼(F • G) 
E)  W ⊃ ∼(F • G)

Question 4

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

Accepted Answer

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

Question 5

Given the argument: P ∨ J / ∼(J • ∼ P) // J ≡ ∼ P
This argument is:

Accepted Answer

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

Question 6

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

Accepted Answer

A) True 
 B)False

Question 7

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

Accepted Answer

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

Question 8

Given the statements: ∼ S ⊃ D / K ⊃ S / D ⊃ K / R ≡ ∼(S • C) / R ≡ C
These statements are:

Accepted Answer

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

Question 9

If an indirect truth table requiring more than one line is constructed for either an argument or a series of statements and a contradiction is derived on the first line, then:

Accepted Answer

A)  The second line must be completed. 
B)  The argument is valid and the statements are consistent. 
C)  The argument is valid and the statements are inconsistent. 
D)  The argument is invalid and the statements are consistent. 
E)  The argument is invalid and the statements are inconsistent.

Question 10

(?W ? L) • (N ? ?R) $\frac { \mathrm { N } \vee \sim \mathrm { W } } { \mathrm { L } \vee \sim \mathrm { R } }$

Accepted Answer

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

Question 11

Given the argument: (K • ∼ C) ⊃ ∼(P • R) / J ⊃ (K • P) / A ⊃ (P • R) // (A • J) ⊃ C
This argument is:

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Harp is soothing if and only if both Miller is not zesty and Coors is not smooth.

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

Statement 1C
Given the following statement:
(H ∨ ∼ K) ≡ (K ⊃ H)
-Statement 1C is:

Accepted Answer

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

Question 17

?S ? ?F $\frac { F } { S }$

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Given the argument: G ⊃ (N • E) / H ⊃ N / K ⊃ ∼E / (H • K) ≡ G
This argument is:

Accepted Answer

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

Question 20

Toyota's closing a factory implies that Fiat improves mileage, given that both Chrysler and Nissan do not increase sales.

Accepted Answer

A)  (∼C • ∼N) ⊃ (T ⊃ F) 
B)  (T ⊃ F) ⊃ (∼C • ∼N) 
C)  ∼(C • N) ⊃ (T ⊃ F) 
D)  T ⊃ [(∼C • ∼N) ⊃ F] 
E)  T ⊃ [F ⊃ (∼C • ∼N)]

Exam 6: Propositional Logic

Statement 3D Given the following statement: (M ⊃ ∼ E) ∨ (R ⊃ E) -Statement 3D is:

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.

If Williams increases enrollment, then not both Fordham and Georgetown expand course offerings.

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

Given the argument: P ∨ J / ∼(J • ∼ P) // J ≡ ∼ P This argument is:

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

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

Given the statements: ∼ S ⊃ D / K ⊃ S / D ⊃ K / R ≡ ∼(S • C) / R ≡ C These statements are:

If an indirect truth table requiring more than one line is constructed for either an argument or a series of statements and a contradiction is derived on the first line, then:

(?W ? L) • (N ? ?R) $\frac { \mathrm { N } \vee \sim \mathrm { W } } { \mathrm { L } \vee \sim \mathrm { R } }$

Given the argument: (K • ∼ C) ⊃ ∼(P • R) / J ⊃ (K • P) / A ⊃ (P • R) // (A • J) ⊃ C This argument is:

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

Harp is soothing if and only if both Miller is not zesty and Coors is not smooth.

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

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

Statement 1C Given the following statement: (H ∨ ∼ K) ≡ (K ⊃ H) -Statement 1C is:

?S ? ?F $\frac { F } { S }$

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

Given the argument: G ⊃ (N • E) / H ⊃ N / K ⊃ ∼E / (H • K) ≡ G This argument is:

Toyota's closing a factory implies that Fiat improves mileage, given that both Chrysler and Nissan do not increase sales.

Exam 6: Propositional Logic

Statement 3D Given the following statement: (M ⊃ ∼ E) ∨ (R ⊃ E) -Statement 3D is:

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.

If Williams increases enrollment, then not both Fordham and Georgetown expand course offerings.

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

Given the argument: P ∨ J / ∼(J • ∼ P) // J ≡ ∼ P This argument is:

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

S ? ?M S∼M\frac{\mathrm{S}}{\sim \mathrm{M}}∼MS​

Given the statements: ∼ S ⊃ D / K ⊃ S / D ⊃ K / R ≡ ∼(S • C) / R ≡ C These statements are:

If an indirect truth table requiring more than one line is constructed for either an argument or a series of statements and a contradiction is derived on the first line, then:

(?W ? L) • (N ? ?R) N∨∼WL∨∼R\frac { \mathrm { N } \vee \sim \mathrm { W } } { \mathrm { L } \vee \sim \mathrm { R } }L∨∼RN∨∼W​

Given the argument: (K • ∼ C) ⊃ ∼(P • R) / J ⊃ (K • P) / A ⊃ (P • R) // (A • J) ⊃ C This argument is:

Q ? ?S SQ\frac { S } { Q }QS​

Harp is soothing if and only if both Miller is not zesty and Coors is not smooth.

?N ? W ∼W∼N\frac { \sim \mathrm { W } } { \sim \mathrm { N } }∼N∼W​

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

Statement 1C Given the following statement: (H ∨ ∼ K) ≡ (K ⊃ H) -Statement 1C is:

?S ? ?F FS\frac { F } { S }SF​

S ? ?C ∼CS\frac{\sim \mathrm{C}}{\mathrm{S}}S∼C​

Given the argument: G ⊃ (N • E) / H ⊃ N / K ⊃ ∼E / (H • K) ≡ G This argument is:

Toyota's closing a factory implies that Fiat improves mileage, given that both Chrysler and Nissan do not increase sales.

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

(?W ? L) • (N ? ?R) $\frac { \mathrm { N } \vee \sim \mathrm { W } } { \mathrm { L } \vee \sim \mathrm { R } }$

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

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

?S ? ?F $\frac { F } { S }$

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