Question 1

(R ⊃ ∼T) • (D ⊃ T)

Accepted Answer

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

Question 2

∼H ⊃ ∼B

Accepted Answer

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

Question 3

Given the pair of statements: R ⊃ ∼ B and ∼ (B • R)
These statements are:

Accepted Answer

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

Question 4

Seiko has a quartz watch if and only if either Movado does not offer a silver dial or Rado does not have a calendar watch; however, Tissot has luminous hands only if both Fossil is water resistant and Rado has a calendar model.

Accepted Answer

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

Question 5

Sierra's being hearty is a necessary condition for both Coors's being smooth and Harp's being crisp; moreover, Guinness is dark if and only if Alaskan's being sweet implies that Beck's is subtle.

Accepted Answer

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

Question 6

∼T ⊃ ∼W

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Suppose an indirect truth table is constructed for an argument, and the truth table requires more than one line. If no contradiction is obtained on the first line, then:

Accepted Answer

A)  The argument is valid. 
B)  The argument could still be valid. 
C)  The argument is invalid. 
D)  The argument is consistent. 
E)  The argument is sound.

Question 9

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

Accepted Answer

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

Question 10

Given the argument: S ≡ (N ∨ H) / S ∨ ∼N // S ⊃ H
This argument is:

Accepted Answer

A)  Invalid; fails in 4th line. 
B)  Invalid; fails in 2nd line. 
C)  Invalid; fails in 5th line. 
D)  Valid. 
E)  Invalid; fails in 3rd line.

Question 11

Not either Regent enlarges its casinos or Celebrity revises its itineraries if Holland remodels its staterooms.

Accepted Answer

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

Question 12

Given the pair of statements: D • ∼ R and R • ∼ D
These statements are:

Accepted Answer

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

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.

Question 14

If dinosaur DNA has deteriorated, then it is impossible to recreate dinosaurs. If dinosaurs perished long ago, then dinosaur DNA has deteriorated. Hence, if dinosaurs perished long ago, then it is impossible to recreate them.

Accepted Answer

A)  Constructive dilemma. 
B)  Affirming the consequent. 
C)  Pure hypothetical syllogism. 
D)  Modus tollens. 
E)  Invalid.

Question 15

Not both Hertz runs a sale and Thrifty lays off workers if either Avis buys new cars or Budget lowers rates.

Accepted Answer

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

Question 16

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

Accepted Answer

A) True 
 B)False

Question 17

If the nuts are stale, then they should not be put into the salad. Thus, the nuts are stale, since they should not be put into the salad.

Accepted Answer

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

Question 18

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.

Question 19

Statement 2F
Given the following statement:
(Q ⊃ ∼ C) • (R ⊃ ∼ Q)
-Statement 2F is:

Accepted Answer

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

Question 20

∼Q

Accepted Answer

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

Exam 6: Propositional Logic

(R ⊃ ∼T) • (D ⊃ T)

∼H ⊃ ∼B

Given the pair of statements: R ⊃ ∼ B and ∼ (B • R) These statements are:

Seiko has a quartz watch if and only if either Movado does not offer a silver dial or Rado does not have a calendar watch; however, Tissot has luminous hands only if both Fossil is water resistant and Rado has a calendar model.

Sierra's being hearty is a necessary condition for both Coors's being smooth and Harp's being crisp; moreover, Guinness is dark if and only if Alaskan's being sweet implies that Beck's is subtle.

∼T ⊃ ∼W

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

Suppose an indirect truth table is constructed for an argument, and the truth table requires more than one line. If no contradiction is obtained on the first line, then:

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

Given the argument: S ≡ (N ∨ H) / S ∨ ∼N // S ⊃ H This argument is:

Not either Regent enlarges its casinos or Celebrity revises its itineraries if Holland remodels its staterooms.

Given the pair of statements: D • ∼ R and R • ∼ D These statements are:

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

If dinosaur DNA has deteriorated, then it is impossible to recreate dinosaurs. If dinosaurs perished long ago, then dinosaur DNA has deteriorated. Hence, if dinosaurs perished long ago, then it is impossible to recreate them.

Not both Hertz runs a sale and Thrifty lays off workers if either Avis buys new cars or Budget lowers rates.

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

If the nuts are stale, then they should not be put into the salad. Thus, the nuts are stale, since they should not be put into the salad.

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

Statement 2F Given the following statement: (Q ⊃ ∼ C) • (R ⊃ ∼ Q) -Statement 2F is:

∼Q