Introduction to Logic solution – conversion, obversion, and contraposition

A.

1. E. Equivalent.

No reckless drivers are people who are considerate of

 

2. A.

Some officers are graduates of West Point.

 

3. I. Equivalent.

Some verpriced and underpowered automobiles are Some European cars

 

4. E. Equivalent.

No warm-blooded animals are reptiles

 

 

5. I. equivalent

Some elderly persons are professional wrestlers.

 

B.

1. I.

Some college athletes are not non-professionals.

 

2. E.

All organic compounds are non-metals.

 

3. O.

Some clergy are non-abstainers.

 

4. E.

All geniuses are non-conformists.

 

5. A.

No objects suitable for boat anchors are non-objects that weigh at least fifteen pounds.

 

C.

1. All non-pessimists are non-journalists.

A. Equivalent.

 

2. Some non-officers are not non-soldiers.

O. Equivalent.

 

3. All degenerates are non-scholars.

A. Equivalent.

 

4. All  non-objects not more than four feet high are non-things weighing less than fifty pounds.

A. Equivalent.

 

5. Some residents are not citizens.

O. Equivalent.

 

D.

All socialists are pacifists. A.

(1) Converse: Some pacifists are socialists. I. (by limitation)

(2) Obverse: No socialists are non-pacifists. E.

(3) Contrapositive: All non-pacifists are non-socialists. A.

No socialists are pacifists. False.

Some socialists are pacifists. True.

Some socialists are not pacifists. False

 

1. Some nonpacifists are not nonsocialists.

Converse of (3) Contrapositive: Some non-socialists are non-pacifists. I. (by limitation)

True.

 

2. No socialists are nonpacifists.

(2) Obverse: No socialists are non-pacifists. E.

True.

 

3. All nonsocialists are nonpacifists.

Undetermined.

 

4. No nonpacifists are socialists.

Converse of (2) Obverse: No non-pacifists are socialists.

True.

 

5. No nonsocialists are nonpacifists.

(2) Obverse: No socialists are non-pacifists.

False.

 

6. All nonpacifists are nonsocialists.

(3) Contrapositive: All non-pacifists are non-socialists. A.

True.

 

7. No pacifists are nonsocialists.

Undetermined.

 

8. Some socialists are not pacifists.

Some socialists are not pacifists. False

 

9. All pacifists are socialists.

(1) Converse: Some socialists are pacifists. I. (by limitation)

Undetermined.

 

10. Some nonpacifists are socialists.

False.

 

E.

No scientists are philosophers. E.

(1) Converse: No philosophers are scientists. E

(2) Obverse: All scientists are non-philosophers. A.

(3) Contrapositive: Some non-philosophers are not non-scientists.

All scientists are philosophers. True.

Some scientists are philosophers. False.

Some scientists are not philosophers. True.

 

1. No nonphilosophers are scientists.

(1) Converse: No philosophers are scientists. E

False.

 

2. Some nonphilosophers are not nonscientists.

True.

 

3. All nonscientists are nonphilosophers.

(2) Obverse: All scientists are non-philosophers.

False.

 

4. No scientists are nonphilosophers.

Converse of (1) Converse: No scientists are philosophers.

False.

 

5. No nonscientists are nonphilosophers.

Contrapositive of (1) Converse: Some non-scientists are not non-philosophers. (by limitation)

Undetermined.

 

6. All philosophers are scientists.

False.

 

7. Some nonphilosophers are scientists.

Converse of (2) Obverse: Some non-philosophers are scientists. (by limitation)

True.

 

8. All nonphilosophers are nonscientists.

False.

 

9. Some scientists are not philosophers.

Some scientists are not philosophers.

True.

 

10. No philosophers are nonscientists.

(1) Converse: No philosophers are scientists.

False.

 

F.

Some saints were martyrs. I.

(1) Converse: Some martyrs were saints.

(2) Obverse: Some saints were not non-martyrs.

(3) Contrapositive: Some non-martyrs were non-saints. Not valid.

No saints were martyrs. False.

 

1. All saints were martyrs.

Some saints were martyrs. subaltern.

Undetermined.

 

2. All saints were nonmartyrs.

False.

 

3. Some martyrs were saints.

(1) Converse.

True.

 

4. No saints were martyrs.

False.

 

5. All martyrs were nonsaints.

Contrapositive of (2) Obverse: Some martyrs were not non-saints.

contradictory.

False.

 

6. Some nonmartyrs were saints.

Undetermined.

 

7. Some saints were not nonmartyrs.

(2) Obverse: Some saints were not non-martyrs.

True.

 

8. No martyrs were saints.

False.

 

9. Some nonsaints were martyrs.

Undetermined.

 

10. Some martyrs were nonsaints.

Undetermined.

 

11. Some saints were not martyrs.

Undetermined.

 

12. Some martyrs were not saints.

Undetermined.

 

13. No saints were nonmartyrs.

Undetermined.

 

14. No nonsaints were martyrs.

Undetermined.

 

15. Some martyrs were not nonsaints.

Obverse of (1) Converse: Some martyrs were not non-saints.

True.

 

G.

Some merchants are not pirates. O.

(1) Converse: Some pirates are not merchants. Not valid.

(2) Obverse: Some merchants are non-pirates. I

(3) Contrapositive: Some non-pirates are not non-merchants. O.

All merchants are pirates. False.

 

1. No pirates are merchants.

Undetermined.

 

2. No merchants are nonpirates.

False.

 

3. Some merchants are nonpirates.

(2) Obverse: Some merchants are non-pirates. I

True.

 

4. All nonmerchants are pirates.

Undetermined.

 

5. Some nonmerchants are nonpirates.

Undetermined.

 

6. All merchants are pirates.

All merchants are pirates. False.

 

7. No nonmerchants are pirates.

Undetermined.

 

8. No pirates are nonmerchants.

Undetermined.

 

9. All nonpirates are nonmerchants.

False.

 

10. Some nonpirates are not nonmerchants.

True.

 

11. Some nonpirates are merchants.

True.

 

12. No nonpirates are merchants.

False.

 

13. Some pirates are merchants.

Undetermined.

 

14. No merchants are nonpirates.

Undetermined.

 

15. No merchants are pirates.

Undetermined.

 

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