Intermediate Logic Week 25

Vocabulary

100

A step by step deduction of a conclusion from a set of premises, each step being justified by a rule of inference or replacement.

Formal Proof of Validity.

200

A valid argument form that can be used to justify a step in a proof. 

rule of inference

300

____________ ___________ is a special rule in a formal proof which allows us to assume the antecedent of a conditional and, once we deduce the consequent, to conclude the entire conditional

Conditional Proof

400

A set of forms of equivalent statements.

Rules of Replacement.

500

A special rule which allows us to assume the negation of a proposition, deduce a self-contradiction, then conclude the proposition.

Reductio ad Absurdum.

Rules of Replacement

100

When a set of statements have the same truth value, they are __________, and can replace each other wherever they occur.

Equivalent.

200

name the rule of replacement being symbolized:

(p > q) = (~q > ~p)

Transposition

300

name the rule of replacement being symbolized:

(p > q) = (~p v q)

Material Implication

400

name the rule of replacement symbolized:

[(p * q) > r] = [p > (q > r)]

Exportation

500

name the rule of replacement symbolized:

~(p * q) = (~p v ~q)

~(p v q) = (~p * ~q)

De Morgan's Theorems

Rules of Inference

100

Name the rule of inference symbolized:

p > q

p

:: q

Modus Ponens

200

name the rule of inference symbolized:

p > q

~q

::~p

Modus Tollens

300

name the rule of inference symbolized:

p

q

:: p * q

Conjunction

400

name the rule of inference being symbolized:

p v q

~p

:: qd

Disjunctive Syllogism

500

name the rule of inference symbolized:

p > q

:: p > (p * q)

Absorption

Practice with Proofs

100

Justify the steps in the proof using rules of inference or replacement:

1. S

2. T v U

3. ~ (S * T)  /  S * U

4. S * (T v U)     _____

5. (S * T) v (S * U)     _____

6. S * U     _____

1, 2 Conj

4 Dist.

5, 3 D.S.

200

Translate the argument into symbolic form using W, G, S:

Either they saw the wizard and it was Gandalf, or they saw the wizard and it was Saruman. It was not Gandalf. It must have been Saruman.

(W * G) v (W * S)

~G   /   ::S

300

Justify the steps in the formal proof of validity using the rules of inference and replacement:

1. (W * G) v (W * S)

2. ~ G   /   :: S

3. W * (G v S) _____

4. (G v S) * W_____

5. G v S _____

6. S _____

1, Dist.

3, Com.

4, Simp.

5, 2, D.S.

400

Justify the following proof using conditional proof:

1. ~A > (B * C)

2. A > D   /   :: ~D > B

3. ~D _____

4. ~A _____

5. B * C _____

6. B _____

7. ~D > B _____

C.P.A

2, 3 M.T

1, 4 M.P

5 Simp.

3-6 C.P

500

Justify the following proof using reductio ad absurdum:

1. (E v ~E) > F   /   :: F

2. ~F   _____

3. ~ (E v ~E)   _____

4. ~E * ~~E   _____

5. F   _____

R.A.A.

1, 2 M.T.

3 DeM

2-4 R.A.

True & False

100

True or False: Every valid argument can be proved using the nine rules of inference. 

False.

200

True or False: You may select one step out of a Conditional Proof to use later on in the proof.

False.

300

True or False: The proposition assumed in C.P.A. (Conditional Proof Assumption) does not need to appear previously in the proof. You can assume anything you wish, as long as you then use it in a conditional proof.

True

400

True or False: Conditional Proof and Reductio Ad Absurdum may be part of a larger proof.

True

500

True or False: When a set of statements have opposite truth values it is called a contradiction.

True.