Question 1

Which of the following states the implicational rule conjunction?

Accepted Answer

A)   p → q, ~p \q
B)   p • q \ p
C)   p, q \ p • q
D)   p \ p ν q C

Question 2

To discharge an assumption is to quit using it in our proof.

Accepted Answer

A) True 
 B)False  True

Question 3

The rule of material equivalence is: (p → q) :: (~p ⋁ q)

Accepted Answer

A) True 
 B)False  True

Question 4

The rule of exportation applies to disjunctions.

Accepted Answer

A) True 
 B)False

Question 5

According to the law of noncontradiction, ~(p • ~p).

Accepted Answer

A) True 
 B)False

Question 6

The law of excluded middle states that for any given syllogism, the middle term drops out.

Accepted Answer

A) True 
 B)False

Question 7

A contingency is the negation of a tautology.

Accepted Answer

A) True 
 B)False

Question 8

We can apply equivalence rules to parts of lines in a proof as well as to entire lines.

Accepted Answer

A) True 
 B)False

Question 9

The rule of distribution tells us that (C ⋁ (B • A)) is logically equivalent to ((C ⋁ B) • (C ⋁ A))

Accepted Answer

A) True 
 B)False

Question 10

All theorems are tautologies.

Accepted Answer

A) True 
 B)False

Question 11

(A • (A → B)) → B is the corresponding conditional for the argument A, A → B \ B.

Accepted Answer

A) True 
 B)False

Question 12

Implicational rules of inference may, within truth-functional logic, be validly applied to parts of compound statements or lines in a proof.

Accepted Answer

A) True 
 B)False

Question 13

Which of the following states the implicational rule hypothetical syllogism?

Accepted Answer

A)   p → q, q → r \ p → r
B)   p ⋁ q, p → r, q → s \ r ⋁ s
C)   p ⋁ q, ~p \q
D)   p → q, ~q \ ~p

Question 14

A single line in a proof may constitute more than one application of a rule or rules of inference.

Accepted Answer

A) True 
 B)False

Question 15

Which of the following is an instance of the rule of disjunctive syllogism?

Accepted Answer

A)   (~p ν ~q) , ~p \ ~q
B)   (~p v ~q) , ~~p \ ~q
C)   ~(p ν ~q) , p \ ~~q
D)   ~(p ν q) , ~p \ ~q)

Question 16

According to the rule of redundancy, we should never repeat any line of a proof.

Accepted Answer

A) True 
 B)False

Question 17

Which of the following is a correct application (or are correct applications) of the rule Material Implication to ~L → ~M?

Accepted Answer

A)   ~~LνM
B)   M ν L
C)   ~~M ν ~~L
D)   both M ν L and ~~M ν ~~L

Question 18

A proof is a series of steps that show how the premises lead, by way of valid rules of inference, to the conclusion.

Accepted Answer

A) True 
 B)False

Question 19

Using which rule can one infer (A ↔ B) using the following statements: (B → A) and (A → B)?

Accepted Answer

A)   material implication
B)   exportation
C)   material equivalence
D)   simplification

Question 20

A proof that employs reductio ad absurdum is a direct proof.

Accepted Answer

A) True 
 B)False

Exam 8: Statement Logic: Proofs

Which of the following states the implicational rule conjunction?

To discharge an assumption is to quit using it in our proof.

The rule of material equivalence is: (p → q) :: (~p ⋁ q)

The rule of exportation applies to disjunctions.

According to the law of noncontradiction, ~(p • ~p).

The law of excluded middle states that for any given syllogism, the middle term drops out.

A contingency is the negation of a tautology.

We can apply equivalence rules to parts of lines in a proof as well as to entire lines.

The rule of distribution tells us that (C ⋁ (B • A)) is logically equivalent to ((C ⋁ B) • (C ⋁ A))

All theorems are tautologies.

(A • (A → B)) → B is the corresponding conditional for the argument A, A → B \ B.

Implicational rules of inference may, within truth-functional logic, be validly applied to parts of compound statements or lines in a proof.

Which of the following states the implicational rule hypothetical syllogism?

A single line in a proof may constitute more than one application of a rule or rules of inference.

Which of the following is an instance of the rule of disjunctive syllogism?

According to the rule of redundancy, we should never repeat any line of a proof.

Which of the following is a correct application (or are correct applications) of the rule Material Implication to ~L → ~M?

A proof is a series of steps that show how the premises lead, by way of valid rules of inference, to the conclusion.

Using which rule can one infer (A ↔ B) using the following statements: (B → A) and (A → B) ?

A proof that employs reductio ad absurdum is a direct proof.