Question 1

A theorem is a statement that

Accepted Answer

A)  can be false only under circumstances specified by the appropriate theory. 
B)  is true only within the context of a specific theory. 
C)  can be proven independently of any premises. 
D)  guarantees the validity of an argument of which it is a premise. 
A)  can be false only under circumstances specified by the appropriate theory. 
B)  is true only within the context of a specific theory. 
C)  can be proven independently of any premises. 
D)  guarantees the validity of an argument of which it is a premise.

Question 2

p ν ~p states which of the following laws?

Accepted Answer

A)  law of excluded middle 
B)  De Morgan's laws 
C)  law of noncontradiction 
D)  law of exclusive dilemma 
A)  law of excluded middle 
B)  De Morgan's laws 
C)  law of noncontradiction 
D)  law of exclusive dilemma

Question 3

The guiding principle of reductio ad absurdum is that

Accepted Answer

A)  whatever implies a contradiction is false. 
B)  systems of natural deduction often lead to absurd conclusions. 
C)  it is not always possible to reduce a set of statements to absurdity. 
D)  often the most straightforward method for deriving a contradiction is by assuming an absurdity. 
A)  whatever implies a contradiction is false. 
B)  systems of natural deduction often lead to absurd conclusions. 
C)  it is not always possible to reduce a set of statements to absurdity. 
D)  often the most straightforward method for deriving a contradiction is by assuming an absurdity.

Question 4

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

Accepted Answer

A)  L → M 
B)  M → L 
C)  ~~M → ~~L 
D)  both M → L and ~~M → ~~L 
A)  L → M 
B)  M → L 
C)  ~~M → ~~L 
D)  both M → L and ~~M → ~~L

Question 5

Which of the following is not a statement of one of the two De Morgan's laws?

Accepted Answer

A)  ~(p ν q) :: (~p • ~q) 
B)  (~p • ~q) :: ~(p ν q) 
C)  (~p ν ~q) :: (~p • ~q) 
D)  ~(p ν q) :: (~p ν ~q) 
A)  ~(p ν q) :: (~p • ~q) 
B)  (~p • ~q) :: ~(p ν q) 
C)  (~p ν ~q) :: (~p • ~q) 
D)  ~(p ν q) :: (~p ν ~q)

Question 6

A theorem is a statement that can be proved independently of any premises.

Accepted Answer

A) True 
 B)False

Question 7

Which of the following is an expression of the rule of material equivalence?

Accepted Answer

A)  (p • (q ν r)) :: ((p • q) ν (p • r)) 
B)  ((p • q) → r) :: (p → (q → r)) 
C)  (p ↔ q) :: ((p → q) • (q → p)) 
D)  (p ν (q • r)) :: ((p • q) ν r) 
A)  (p • (q ν r)) :: ((p • q) ν (p • r)) 
B)  ((p • q) → r) :: (p → (q → r)) 
C)  (p ↔ q) :: ((p → q) • (q → p)) 
D)  (p ν (q • r)) :: ((p • q) ν r)

Question 8

Any argument that has a theorem as a premise is valid, regardless of the conclusion.

Accepted Answer

A) True 
 B)False

Question 9

According to contraposition (the equivalence rule), ~A → ~B is logically equivalent to B →
A. True False

Accepted Answer

A) True 
 B)False

Question 10

Which of the following is an expression of the law of noncontradiction?

Accepted Answer

A)  p ν ~p 
B)  p • ~p 
C)  ~(p → ~p) 
D)  ~(p • ~p) 
A)  p ν ~p 
B)  p • ~p 
C)  ~(p → ~p) 
D)  ~(p • ~p)

Question 11

Which of the following is an expression of the rule of distribution?

Accepted Answer

A)  (p ν (q • r)):: ((p ν q) • (p ν r)) 
B)  p:: p • p 
C)  ~(p • q):: (~p ν ~q) 
D)  ((p • q) → r):: (p → (q → r)) 
A)  (p ν (q • r)):: ((p ν q) • (p ν r)) 
B)  p:: p • p 
C)  ~(p • q):: (~p ν ~q) 
D)  ((p • q) → r):: (p → (q → r))

Question 12

Conjunction is an equivalence rule.

Accepted Answer

A) True 
 B)False

Question 13

p :: (p • p) expresses which rule of equivalence?

Accepted Answer

A)  conjunction 
B)  distribution 
C)  commutation 
D)  redundancy 
A)  conjunction 
B)  distribution 
C)  commutation 
D)  redundancy

Question 14

An indirect proof is a proof that makes use of assumptions.

Accepted Answer

A) True 
 B)False

Question 15

The rule of addition indicates that if we have a disjunction, we may validly infer the denial of one of its disjuncts.

Accepted Answer

A) True 
 B)False

Question 16

The basic idea behind conditional proof is that we can prove a conditional

Accepted Answer

A) True 
 B)False

Question 17

Which of the following states the implicational rule constructive dilemma?

Accepted Answer

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

Question 18

The rule of conjunction indicates that if we have a conjunction, you may validly infer either conjunct.

Accepted Answer

A) True 
 B)False

Question 19

Using which rule can one infer (A ν (B • C)) using the following statement: (A ν B) • (A ν C)?

Accepted Answer

A)  simplification 
B)  distribution 
C)  association 
D)  redundancy 
A)  simplification 
B)  distribution 
C)  association 
D)  redundancy

Question 20

p → q, p \ q is the implicational rule

Accepted Answer

A)  modus tollens. 
B)  modus ponens. 
C)  constructive dilemma. 
D)  simplification. 
A)  modus tollens. 
B)  modus ponens. 
C)  constructive dilemma. 
D)  simplification.

A theorem is a statement that

p ν ~p states which of the following laws?

The guiding principle of reductio ad absurdum is that

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

Which of the following is not a statement of one of the two De Morgan's laws?

A theorem is a statement that can be proved independently of any premises.

Which of the following is an expression of the rule of material equivalence?

Any argument that has a theorem as a premise is valid, regardless of the conclusion.

According to contraposition (the equivalence rule), ~A → ~B is logically equivalent to B → A. True False

Which of the following is an expression of the law of noncontradiction?

Which of the following is an expression of the rule of distribution?

Conjunction is an equivalence rule.

p :: (p • p) expresses which rule of equivalence?

An indirect proof is a proof that makes use of assumptions.

The rule of addition indicates that if we have a disjunction, we may validly infer the denial of one of its disjuncts.

The basic idea behind conditional proof is that we can prove a conditional

Which of the following states the implicational rule constructive dilemma?

The rule of conjunction indicates that if we have a conjunction, you may validly infer either conjunct.

Using which rule can one infer (A ν (B • C)) using the following statement: (A ν B) • (A ν C)?

p → q, p \ q is the implicational rule

Basic Concepts

Identifying Arguments

Logic and Language

Informal Fallacies

Categorical Logic: Statements

Categorical Logic: Syllogisms

Statement Logic: Truth Tables

Predicate Logic

Inductive Logic

Filters

Exam 8: Statement Logic: Proofs

A theorem is a statement that

p ν ~p states which of the following laws?

The guiding principle of reductio ad absurdum is that

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

Which of the following is not a statement of one of the two De Morgan's laws?

A theorem is a statement that can be proved independently of any premises.

Which of the following is an expression of the rule of material equivalence?

Any argument that has a theorem as a premise is valid, regardless of the conclusion.

According to contraposition (the equivalence rule), ~A → ~B is logically equivalent to B → A. True False

Which of the following is an expression of the law of noncontradiction?

Which of the following is an expression of the rule of distribution?

Conjunction is an equivalence rule.

p :: (p • p) expresses which rule of equivalence?

An indirect proof is a proof that makes use of assumptions.

The rule of addition indicates that if we have a disjunction, we may validly infer the denial of one of its disjuncts.

The basic idea behind conditional proof is that we can prove a conditional

Which of the following states the implicational rule constructive dilemma?

The rule of conjunction indicates that if we have a conjunction, you may validly infer either conjunct.

Using which rule can one infer (A ν (B • C)) using the following statement: (A ν B) • (A ν C)?

p → q, p \ q is the implicational rule

Basic Concepts

Identifying Arguments

Logic and Language

Informal Fallacies

Categorical Logic: Statements

Categorical Logic: Syllogisms

Statement Logic: Truth Tables

Predicate Logic

Inductive Logic

Filters