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Lecture 4

This

**preview**shows pages 1-2. to view the full**7 pages of the document.**Assignment 4:

Part 1:

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[44-1] Exercise designed to appreciate comparative merit of CP:

with the same argument below,

[44-1.1] do the 1st proof without using CP; &

[44-1.2] do the 2nd proof by using CP:

44-1.1:

C: M -> R

1: ~M V N

2: ~R -> ~N

3: M -> N 1 Impl

4: N -> R 2 Contra

5: M -> R 3,4 HS ... QED

44-1.2:

C: M -> R

1: ~M V N

2: ~R -> ~N

-->3: M AP

4: N 1,3 DS

5: R 2,4 MT

6: M->R 3-5 CP ... QED

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[44-2] Exercise designed to employ CP as part of the whole proc ess:

with the same argument below,

[44-2.1] do the 1st proof by using CP with ~P as AP

[44-2.2] do the 2nd proof by using CP with R as AP; & then Contra

[44-2.1]

C: ~P -> ~R

1: R -> (L & S)

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2: (L V M) -> P

--> 3: ~P AP

| 4: ~(L V M) 2,3 MT

| 5: ~L & ~M 4 DeM

| 6: ~L 5 Simp

| 7: ~L V ~S 6 Add

| 8: ~(L & S) 7 DeM

| 9: ~R 1,8 MT

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10: ~P -> ~R 3-9 CP .... QED

[44-2.2]

C: ~P -> ~R

1: R -> (L & S)

2: (L V M) -> P

--> 3: R AP (to get P)

| 4: L & S 1,3 MP

| 5: L 4 Simp

| 6: L V M 5 Add

| 7: P 2,6 MP

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8: R -> P 3-7 CP

9: ~P -> ~R 8 Contra ... QED

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[44-3] Exercise designed to see CP as a self-contained module:

use CP to the get the 1st part of conjunction;

use the conditional as a premise to get the 2nd part; &

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