Introductory Logic Exercises: Lessons 24-26

Form

100

All oats are grain.
Some grains are rice.
Therefore, some rice is oats.

AII-4

200

All gorillas are mammals.
Some apes are gorillas.
Therefore, some apes are not mammals. 

AIO-1

300

Some harps are not pianos.
No harps are grand pianos.
Therefore, some grand pianos are not pianos.

OEO-3

400

Some fruits are bananas.
No bananas are apples.
Therefore, some apples are not fruit. 

IEO-4

500

Some wheeled vehicles are not motorcycles.
Some airplanes are wheeled vehicles.
Therefore, all airplanes are motorcycles. 

OIA-1

Mood

100

Some chanting story-tellers are rap singers. 

I

200

No mid-management secretaries are secret agents. 

E

300

All chanting story-tellers are bards. 

A

400

Some graduates of medical school are professional nurses. 

I

500

Some robots are not programmed humanoids. 

O

Figure

100

Some fruits are bananas.
No bananas are apples.
Therefore, some apples are not fruit. 

4

200

All gorillas are mammals.
Some apes are gorillas.
Therefore, some apes are not mammals. 

1

300

All oats are grain.
Some grains are rice.
Therefore, some rice is oats.

4

400

Some harps are not pianos.
No harps are grand pianos.
Therefore, some grand pianos are not pianos.

3

500

No reptiles are mammals.
All apes are mammals.
Therefore, some apes are reptiles. 

2

Validity

100

All cherries are fruit.
All maraschinos are cherries.
Therefore, all maraschinos are fruit. 

Valid

AAA-1

200

All apples are fruit.
All bananas are fruit.
Therefore, all apples are bananas. 

INVALID. 

AAA-2

Undistributed Middle

300

No cherries are meat.
All hotdogs are meat.
Therefore, no hotdogs are cherries. 

VALID

EAE-2

400

No meat is fruit.
All meat is an edible thing.
Therefore, no edible things are fruit. 

INVALID

EAE-3

Illicit Minor (edible thing distributed in conclusion, but not in premise)

500

Some cherries are not sweet-tasting things.
All cherries are fruits.
Therefore, some fruits are not sweet-tasting things.  

VALID

OAO-3

Fallacy

100

All P are M.
All S are M.
Therefore, all S are P. 

Undistributed Middle

200

No P is M.
No S is M.
There all S is P. 

Two Negative Premises
Negative Premise and an Affirmative Conclusion

300

All M are P.
All S are M.
Therefore, some S are not P. 

Illicit Major
Two Affirmative Premises and a Negative Conclusion

400

All M is P.
No S is M.
Therefore, some S is P. 

Negative Premise and an Affirmative Conclusion

500

Some P are not M.
Some S are not M.
Therefore, some S are not P. 

Illicit Major

Two Negative Premises