### Question Description

I need to do the exercises 12 & 13. they are basic logic let me know if you can help.

thanks,

Linnet

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## Final Answer

Attached.

Running head: RULES OF INFERENCE

Rules of Inference

Student’s Name

Institution Affiliation

RULES OF INFERENCE

1

Rules of Inference

Lesson 12

Exercise 1

a)

1. A→ B used MP rule

2. B→ C used MP rule

3. A→ C used DS rule

b)

1. A in this case A is a premise

2. A→ B used MP rule

3. A→ B used MP rule

c)

1. - B used MT rule

2. A→ B used MP rule

3. - A used MP rule

d)

1. A→ B used MP rule

2. - B used DS rule

3. – A in this case –A is a premise

e)

1. - B used DS rule

2. C→ B used DS rule

3. – C used MT rule

f)

1. - B used DS rule

RULES OF INFERENCE

2

2. A v B used MP rule

3. A in this case A is a premise

Exercise 3

a)

If James receives the parcel before I go, he will share with me whatever it contains.

The generosity of James helped me in saving the few cents I had planned to buy a book; James

shared the parcel items with me.

1. K( A v B)

2. - S & K

3. K

I derived K from the second line through Simplification,

4. A v B

I derived A v B from lines 1 & 2 by Modus Ponens, MP

b)

I can decide to take salad or I can decide to take soup.

I will not decide salad and therefore I will decide soup.

1. A v B

(It is either I decide to take salad or soup)

2. - B & - C

3. –C

4.

I derived –C from the first and third line using the Simplification method

AvB

I derived A v B from lines 3 and 1 using the Disjunction Syllogism, DS

c)

1. - A &- B

2.

AvD

3. –B

4.

2, Simp

–A v –B 1, 2

HS

d)

1. A& (B C)

(I derived –B from line 4 through Simplfication)

(I derived –A v –B from lines 1 and 2 using Hypothetical Syllogism,

RULES OF INFERENCE

3

2. A M

3. A&

1, 2 Simp

4. B C 1 & 2

(I derived A& from the first and second by Simlification

(I used Modus Tollens, MT in deriving B C from lines 1 and 2.

Lesson 13

Exercise 1

a)

1. A v B

2. – B

3. A

In this case, A was derived from line 1 by Modus Ponens

b)

1. A B

2. B - C

3. A - C

-C was derived from line 1 and 2 by Disjunction Syllogism

c)

1. – ( A v B )

_________________

2. – A & - B

-A & -B was derived from line 1 by De Morgan’s Laws because –A v –B is logically equivalent

to –(A B)

d)

1. A B

2. – B

RULES OF INFERENCE

3. – A

-B was derived from line 2 by Modus Tulles and –A was derived from line 1 by Modus Ponens

e)

1. A & B

2. A

A was derived from line 1 through Modus Ponens

f)

1. A v (B& C)

2. – (B& C)

3. A

-(B &C) was derived from line 2 a...

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