Exercise 4.4

Part I

1. No Non-B are A. True

2. Some non-B are non-A. Und.

3. No A are B. False

4. All non-B are A. False

5. Some B are not non-A. Und.

6. Some non-A are not B. True

7. Contraposition Und.

8. Obversion True

9. Conversion Und.

10. Obversion False

11. Contraposition True

12. Conversion False

Part II

1a. All potential causes of lung cancer are homes contaminated by radon gas. (Not logically equivalent).

b. No completely successful procedures are sex-change operations. (Logically equivalent).

c. Some works that celebrate the revolutionary spirit are murals by Diego Rivera. (Logically equivalent).

d. Some substances with a crystalline structure are not forms of carbon. (Not logically equivalent).

2a. No radically egalitarian societies are societies that preserve individual liberties. (Logically equivalent).

b. All cult leaders are people who brainwash their followers. (Logically equivalent).

c. Some college football coaches are not persons who slip money to their players. (Logically equivalent).

d. Some budgetary cutbacks are actions unfair to the poor. (Logically equivalent).

3a. All physicians eligible to practice are physicians whose licenses are intact. (Logically equivalent).

b. No compressible substances are non-gasses. (Not logically equivalent).

c. Some scientists who believe in a final particle theory are scientists who do not back the supercollider. (Not logically equivalent).

d. Some people who advocate integrated schools are not people who support mandatory bussing. (Logically equivalent).

Part III

1. Invalid (illicit conversion).

2. Valid.

3. Valid.

4. Invalid (illicit contraposition).

5. Valid.

6. Valid.

7. valid.

8. Invalid (illicit conversion).

9. Invalid (illicit contraposition).

10. valid.

Part IV

1. Some I are not H.

I H

F: No H are I.

Invalid.

I H

2. All C are non-P.

C P

F: Some P are C.

Valid.

C P

3. Some G are P

G P

No non-P are G.

Invalid.

G P

4. F: All G are non-M.

G M

Some M are not non-G.

Valid.

G M

5. F: Some non-T are not non-P.

T P

All P are T.

Valid.

T P

6. F: Some H are not P.

H P

Some non-P are H.

Invalid.

H P

7. F: Some S are not P.

S P

Some P are non-S.

Invalid.

S P

8. All P are S

P S

No S are non-P.

Invalid.

P S

9. Some non-P are S.

P S

F: All S are P.

Valid.

P S

10. No non-P are non-M.

P M

No P are M.

Invalid.

P M

11. F: Some F are not non-L.

F L

No L are F.

Valid.

F L

12. Some P are E.

P E

Some non-E are non-P.

Invalid.

P E

13. No R are F.

R F

F: Some F are not non-R.

Valid.

R F

14. F: All non-C are non-P.

C P

Some P are not C.

Valid.

C P

15. F: No A are non-U.

A U

Some U are non-A.

Invalid.

A U

Exercise 4.4

Part I

1. No Non-B are A. True

2. Some non-B are non-A. Und.

3. No A are B. False

4. All non-B are A. False

5. Some B are not non-A. Und.

6. Some non-A are not B. True

7. Contraposition Und.

8. Obversion True

9. Conversion Und.

10. Obversion False

11. Contraposition True

12. Conversion False

Part II

1a. All potential causes of lung cancer are homes contaminated by radon gas. (Not logically equivalent).

b. No completely successful procedures are sex-change operations. (Logically equivalent).

c. Some works that celebrate the revolutionary spirit are murals by Diego Rivera. (Logically equivalent).

d. Some substances with a crystalline structure are not forms of carbon. (Not logically equivalent).

2a. No radically egalitarian societies are societies that preserve individual liberties. (Logically equivalent).

b. All cult leaders are people who brainwash their followers. (Logically equivalent).

c. Some college football coaches are not persons who slip money to their players. (Logically equivalent).

d. Some budgetary cutbacks are actions unfair to the poor. (Logically equivalent).

3a. All physicians eligible to practice are physicians whose licenses are intact. (Logically equivalent).

b. No compressible substances are non-gasses. (Not logically equivalent).

c. Some scientists who believe in a final particle theory are scientists who do not back the supercollider. (Not logically equivalent).

d. Some people who advocate integrated schools are not people who support mandatory bussing. (Logically equivalent).

Part III

1. Invalid (illicit conversion).

2. Valid.

3. Valid.

4. Invalid (illicit contraposition).

5. Valid.

6. Valid.

7. valid.

8. Invalid (illicit conversion).

9. Invalid (illicit contraposition).

10. valid.

Part IV

1. Some I are not H.

I H

F: No H are I.

Invalid.

I H

2. All C are non-P.

C P

F: Some P are C.

Valid.

C P

3. Some G are P

G P

No non-P are G.

Invalid.

G P

4. F: All G are non-M.

G M

Some M are not non-G.

Valid.

G M

5. F: Some non-T are not non-P.

T P

All P are T.

Valid.

T P

6. F: Some H are not P.

H P

Some non-P are H.

Invalid.

H P

7. F: Some S are not P.

S P

Some P are non-S.

Invalid.

S P

8. All P are S

P S

No S are non-P.

Invalid.

P S

9. Some non-P are S.

P S

F: All S are P.

Valid.

P S

10. No non-P are non-M.

P M

No P are M.

Invalid.

P M

11. F: Some F are not non-L.

F L

No L are F.

Valid.

F L

12. Some P are E.

P E

Some non-E are non-P.

Invalid.

P E

13. No R are F.

R F

F: Some F are not non-R.

Valid.

R F

14. F: All non-C are non-P.

C P

Some P are not C.

Valid.

C P

15. F: No A are non-U.

A U

Some U are non-A.

Invalid.

A U