# rules if inference

Part

1

Complete

the

logical

proof

for

each

of

the

following

arguments

using

the

18

rules

of

inference.

Provide

the

justification

(line

numbers

needed

for

the

derivation

and

rule

of

inference)

for

each

step

of

the

proof.

Argument

1

1. P

âŠƒ

Q

2. (R

â€¢

S)

âŠƒ

P

3. R

:

.

S

âŠƒ

Q

4. (R

â€¢

S)

âŠƒ

Q

5. âˆ¼(R

â€¢

S)

âˆ¨

Q

6. (âˆ¼R

âˆ¨

âˆ¼S)

âˆ¨

Q

7. âˆ¼R

âˆ¨

(âˆ¼S

âˆ¨

Q)

8. R

âŠƒ

(âˆ¼S

âˆ¨

Q)

9. (âˆ¼S

âˆ¨

Q)

10. S

âŠƒ

Q

Argument

2

1. T

âˆ¨

S

2. âˆ¼T

3. (S

âˆ¨

S)

âŠƒ

(âˆ¼P

âˆ¨

R)

:

.

âˆ¼R

âŠƒ

âˆ¼P

4. S

5. S

âˆ¨

S

6. âˆ¼P

âˆ¨

R

7. R

âˆ¨

âˆ¼P

8. âˆ¼R

âŠƒ

âˆ¼P

Chapter

8:

Logical

Proofs

Homework

Part

2

Complete

the

logical

proof

for

each

of

the

following

arguments

using

the

18

rules

of

inference.

Provide

the

derivation

for

each

step

of

the

proof

given

its

justification

(line

numbers

needed

for

the

derivation

and

rule

of

inference).

Argument

1

1. âˆ¼P

2. âˆ¼Q

âŠƒ

P

3. âˆ¼Q

âˆ¨

(âˆ¼P

âŠƒ

R)

:

.

R

âˆ¨

S

4.

2,

1

MT

5.

3

Impl

6.

5,

4

MP

7.

6,

1

MP

8.

7

Add

Argument

2

1. P

âŠƒ

(âˆ¼Q

â€¢

R)

2. R

âŠƒ

Q

:

.

âˆ¼P

3.

2

Impl

4.

3

DM

5.

4

Com

6.

1,5

MT

Chapter

8:

Logical

Proofs

Homework

Part

3

Construct

a

logical

proof

for

each

of

the

following

arguments

using

the

18

rules

of

inference.

Provide

the

derivation

for

each

step

of

the

proof

given

its

justification

(line

numbers

needed

for

the

derivation

and

rule

of

inference).

Argument

1

1. âˆ¼P

2. (Q

âˆ¨

P)

âˆ¨

R

:

.

Q

âˆ¨

R

Argument

2

1. âˆ¼(P

â€¢

P)

:

.

P

âŠƒ