Module Five

Which of the following is a correct application of the equivalence rule commutation?

(A ν B) • C \ C • (A ν B)

Which of the following is a correct application of the equivalence rule distribution

A ν (B • C) \ (A ν B) • (A ν C)

Which of the following arguments is an instance of modus ponens?

C • B, (C • B) → (D ν E) \ D ν E

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

False

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

False

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

False

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

False

The rule of modus ponens indicates that if we have a conditional statement and the affirmation of its consequent, we may validly infer its antecedent.

False

The rule of modus tollens indicates that if we have a conditional and then denial of its antecedent, we may validly infer the denial of its consequent.

False

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

True

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

True

Hypothetical syllogism is an implicational rule.

True

If an assumption for a conditional proof has been discharged, it cannot be used in subsequent lines of the proof.

True

The basic principle underlying reductio ad absurdum is that whatever implies a contradiction is false.

True

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

True

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

True

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

both M → L and ~~M → ~~L

A theorem is a statement that

can be proven independently of any premises

p → q, p \ q is the implicational rule

modus ponens

Which of the following states the implicational rule constructive dilemma?

p ν q, p → r, q → s \ r ν s

Which of the following states the implicational rule hypothetical syllogism?

p → q, q → r \ p → r

Which of the following states the implicational rule conjunction?

p, q \ p • q

The basic idea behind conditional proof is that

we can prove a conditional true by assuming that its antecedent is true and showing that its consequent can be derived from that assumption

The guiding principle of reductio ad absurdum is that

whatever implies a contradiction is false

Which of the following is a correct replacement for (D • C) → ~(A ⋁ B) using material implication?

~(D • C) ν ~(A ⋁ B)