Logic Exercises
Exercise #1 Identify the terms within statements
Identify the subject term, the predicate term, copula and quantifiers (if any):
1. Some men are happily married.
2. All bats are members of the class of rodents.
3. James is wicked.
4. Horses are man’s best friend.
5. Some tables are not mahogany.
6. Nothing green is in the room.
Logic Exercises
Answers Exercise #1
Identify the subject term, the predicate term, copula and quantifiers (if any):
S = subject term; P = predicate; C = copula; Q = quantifier
Q
S
1. Some men are
Q
S
2. All bats
C
are
S
C
3. James is
S
C
4. Horses are
Q
S
5. Some tables
C
P
happily married.
P
members of the class of rodents.
P
wicked.
P
man’s best friend.
C
P
are not mahogany.
Q
S
C
P
6. Nothing green is in the room.
Logic Exercises
Exercise #2
Determine the following sentences to be affirmative or negative.
1. James is very unhappy.
2. Lions are not untrustworthy.
3. She was not disinclined to come.
4. He has been unwell for months now.
5. Some philosophers are intuitive.
6. No non-addicts can understand the problem.
7. All non -S are non-P.
Logic Exercises
Exercise #2 Answers
Determine the following sentences to be affirmative or negative.
1. James is very unhappy.
affirmative
2. Lions are not untrustworthy.
negative
3. She was not disinclined to come.
negative
4. He has been unwell for months now.
affirmative
5. Some philosophers are intuitive.
affirmative
6. No non-addicts can understand the problem.
negative
7. All non -S are non-P.
affirmative
Logic Exercises
Exercise #3
Determine whether the following sentences are universal or particular.
1. Fish are mammals.
2. Some dragons are fierce.
3. This table is brown.
4. That system is useless.
5. They are crazy.
6. Hard-working students are successful.
7. Albert Einstein was a genius.
8. Those tins seem heavy.
9. That bottle of aspirin is not full.
10. No human beings are infallible.
11. Some cats are not wise.
12. Men have climbed Mount Everest.
13. All police are not cruel.
14. All golfers are wealthy.
15. Some babies are small.
Logic Exercises
Exercise #3 Answers
Determine whether the following sentences are universal or particular.
1. Fish are mammals.
universal
2. Some dragons are fierce.
particular
3. This table is brown.
universal
4. That system is useless.
universal
5. They are crazy.
universal
6. Hard-working students are successful.
universal
7. Albert Einstein was a genius.
universal
8. Those tins seem heavy.
universal
9. That bottle of aspirin is not full.
universal
10. No human beings are infallible.
universal
11. Some cats are not wise.
particular
12. Men have climbed Mount Everest.
particular
13. All police are not cruel.
particular
14. All golfers are wealthy.
universal
15. Some babies are small.
Particular
Logic Exercises
Exercise #4
Determine whether the following sentences are to be designated as A, E, I, or O,
and determine their quantity and quality.
1. No Americans are explorers.
2. All doctors are interested in medicine.
3. Some lawyers are golfers.
4. Muhammad Ali is no longer heavy-weight champion.
5. Martin Luther King Jr. was a champion of freedom.
6. Some conductors are non-luminous.
7. All football players are excluded from the class of authors.
8. Some tennis players are not authors.
9. That paper was well-read.
10. Each and every lion is ferocious.
Logic Exercises
Exercise #4
Answers
Determine whether the following sentences are to be designated as A, E, I, or O,
and determine their quantity and quality.
1. No Americans are explorers.
E, Universal - negative
2. All doctors are interested in medicine.
A, Universal - affirmative
3. Some lawyers are golfers.
I, Particular - affirmative
4. Muhammad Ali is no longer heavy-weight champion.
E, Universal - negative
5. Martin Luther King Jr. was a champion of freedom. A, Universal affirmative
6. Some conductors are non-luminous.
I, particular - affirmative
7. All football players are excluded from the class of authors.
E, universal - negative
8. Some tennis players are not authors.
O, particular - negative
9. That paper was well-read.
A, universal - affirmative
10. Each and every lion is ferocious.
A, universal - affirmative
Logic Exercises
Exercise #5
Indicate which terms are distributed and which terms are undistributed. “D” will
stand for distributed, and “U” will stand for undistributed.
1. All Canadians are good swimmers.
2. No conductors are overpaid.
3. Some swans are not black.
4. Some swans are beautiful.
5. Cindy Crawford is a model.
6. All Manitobans are non-farmers.
7. Some Albertans are not farmers.
Logic Exercises
Exercise #5
Answers
Indicate which terms are distributed and which terms are undistributed. “D” will
stand for distributed, and “U” will stand for undistributed.
D
1. All Canadians are
U
good swimmers.
D
2. No conductors are
D
overpaid.
U
3. Some swans are
U
4. Some swans are
D
not
black.
U
beautiful.
D
5. Cindy Crawford is
U
a model.
D
6. All Manitobans are
U
non-farmers.
U
7. Some Albertans are
not
D
farmers.
Logic Exercises
Exercise #6
Identifying terms: Major, Minor, Middle
Identify the major, middle, and minor terms of the following syllogisms, and
designate the major and minor premises.
Use “M” for middle term; “Ma” for major term; and “Mi” for minor term.
1.
All men are fallible.
I am a man.
Therefore, I am fallible.
2. Some politicians are ignoble.
No one who is ignoble is wise.
Some politicians are not wise.
3. All singers are temperamental.
No truck drivers are temperamental.
No singers are truck drivers.
4. All S is M.
No M is P.
______________________
No S is P.
5. Some S is M.
Some P is M.
____________________
Some S is P.
Logic Exercises
Exercise #6
Identifying terms: Major, Minor, Middle
Answers
Identify the major, middle, and minor terms of the following syllogisms, and
designate the major and minor premises.
Use “M” for middle term; “Ma” for major term; and “Mi” for minor term.
M
Ma
1. All men are fallible. (Major premise)
Mi
I am a
M
man.
(Minor premise)
Mi
Ma
Therefore, I am fallible.
2.
Mi
M
Some politicians are ignoble. (Minor premise)
M
Ma
No one who is ignoble is wise.
(Major premise)
Mi
Ma
Some politicians are not wise.
Mi
3. All singers are
M
temperamental. (Minor premise)
Ma
M
No truck drivers are temperamental. (Major premise)
Mi
No singers are
Mi
4. All S is
Ma
truck drivers.
M
M.
(minor premise)
M
Ma
No M is P.
(major premise)
______________________
Mi
Ma
No S is
P.
Mi
5. Some S is
M
M. (minor premise)
Ma
M
Some P is
M. (major premise)
_____________________
Mi
Ma
Some S is
P.
Logic Exercises
Exercise #7
Determine whether the following syllogisms are valid or invalid. If invalid,
state the fallacy they commit, or the rule they break.
1.
All accountants are tennis players.
All youngsters are tennis players.
Therefore, all accountants are youngsters.
2.
All plants are substances.
All animals are substances.
Therefore, all plants are animals.
3.
All poets have creative imagination.
No poets are good businessmen.
Therefore, no good businessmen have creative imagination.
4.
Some modern poetry is interesting.
Everything interesting has value,
Nothing which has value is worthless,
Some modern poetry is not worthless.
5.
All Buddhists are vegetarians,
George Bernard Shaw is a vegetarian,
Therefore, George Bernard Shaw is a Buddhist.
6.
Some Moslems are non-drinkers,
All Arabs are Moslems,
Some Arabs are non-drinkers.
7.
All baseball players are well paid,
Some teachers of philosophy are not baseball players,
Some teachers of philosophy are not well paid.
8.
Some bus riders are alcoholics,
Some train riders are not alcoholics,
Some bus riders are train riders.
9.
No Germans are democrats,
Some democrats are not fascists,
Some Germans are not fascists.
10.
Some teeth are not white,
All white things are beautiful.
Some beautiful things are not teeth.
Logic Exercises
Exercise #7
Answers
1.
All accountants are tennis players.
All youngsters are tennis players.
Therefore, all accountants are youngsters. Invalid: Undistributed middle
2.
All men are substances.
All animals are substances.
Therefore, all men are animals.
Invalid: Undistributed middle
3.
All poets have creative imagination.
No poets are good business men.
Therefore, no good business men have creative imagination.
Invalid: Illicit process, term distributed in conclusion NOT distributed in premise
4.
Some modern poetry is interesting.
Everything interesting has value,
Nothing which has value is worthless,
More than three terms, not
Some modern poetry is not worthless.
a syllogism.
5.
6.
7.
8.
9.
10.
All Buddhists are vegetarians,
George Bernard Shaw is a vegetarian,
Therefore, George Bernard Shaw is a Buddhist.
Some Moslems are non-drinkers,
All Arabs are Moslems,
Some Arabs are non-drinkers.
Invalid: undistributed
middle
Invalid: Undistributed middle.
All baseball players are well paid,
Some teachers of philosophy are not baseball players, Invalid: Illicit
process
Some teachers of philosophy are not well paid.
(term in conclusion
distributed, but not in
premises)
Some bus riders are alcoholics,
Some train riders are not alcoholics,
Invalid: affirmative
Some bus riders are train riders.
Conclusion, from
Negative premise
No Germans are democrats,
Some democrats are not fascists,
Invalid: no conclusion
Some Germans are not fascists.
from 2 negative premises
Some teeth are not white,
Invalid: Illicit process term
All white things are beautiful.
distributed in conclusion, but not
Some beautiful things are not teeth. In premises)
Logic Exercises
Exercise #8
Put the following into standard logical form.
1. Ships are beautiful.
2. Joan is a blonde.
3. The whale is a mammal.
4. Whoever is a child is silly.
5. Snakes coil.
6. None but golfers appreciate Hogan.
7. Only indicative sentences make assertions.
8. Nothing ventured, nothing gained.
9. All but the brave die many deaths.
10. All swans are not white.
Logic Exercises
Exercise #8
Answers
Put the following into standard logical form.
1. Ships are beautiful.
All (or some) ships are beautiful things.
2. Joan is a blonde.
Joan is a blonde woman.
3. The whale is a mammal.
All whales are mammals.
4. Whoever is a child is silly.
All children are silly creatures.
5. Snakes coil.
All snakes are coiling things.
6. None but golfers appreciate Hogan.
All persons who appreciate Hogan are golfers.
7. Only indicative sentences make assertions.
All assertions are made by indicative sentences.
8. Nothing ventured, nothing gained.
No non-ventured things are gained things.
9. All but the brave die many deaths.
Nothing which is a brave thing dies many deaths,
or
All things which are not brave things are things which die many deaths.
10. All swans are not white.
Some swans are not white.
Logic Exercises
Exercise # 9
A.
Obvert the following:
1.
Some San Franciscans are braggarts.
2.
No trains are buses.
3.
Some magazines are not articulate.
4.
Only dwarfs are kind.
5.
All fairies are immortal.
6.
All except John will be admitted.
7.
Whoever is intelligent is appreciated.
B.
Convert the following:
1.
Some cats are white.
2.
No lions are tame.
3.
Some Russians are not Communists.
4.
All non-conductors are non-metallic.
5.
All automobiles are expensive.
6.
Some golfers are champions.
7.
Some automobiles are not expensive.
8.
Nothing ventured, nothing gained.
Logic Exercises
Exercise # 9
Answers.
A.
Obvert the following:
1.
Some San Franciscans are braggarts.
Some San Franciscans are not non-braggarts.
2.
No trains are buses.
All trains are non-buses
3.
Some magazines are not articulate.
Some magazines are non-articulate.
4.
Only dwarfs are kind.
No kind persons are non-dwarfs.
5.
All fairies are immortal.
No fairies are mortal.
6.
All except John will be admitted.
No one who is not John is a non-admitted person.
7.
Whoever is intelligent is appreciated.
No one who is intelligent is a non-appreciated person.
B.
Convert the following:
1.
Some cats are white.
Some white things are cats.
2.
No lions are tame.
No tame creatures are lions.
3.
Some Russians are not Communists.
O statement, cannot be converted.
4.
All non-conductors are non-metallic.
Some non-metallic things are non-conductors
5.
All automobiles are expensive.
Some expensive things are automobiles.
6.
Some golfers are champions.
Some champions are golfers.
7.
Some automobiles are not expensive.
O statement, cannot be converted.
8.
Nothing ventured, nothing gained.
Nothing gained, nothing ventured.
Logic Exercises
Exercise #10
Identify the fallacies committed in the following:
1. Water the plant when thoroughly potted.
2. He:
She:
He:
Dance?
Love to!
Marvelous, that’s better than dancing.
3. Jones was not intoxicated today.
4. Your contention that alcohol is injurious is without merit since you drink.
5. It has been argued that the Crusades were a noble endeavor, since men of
high purpose founded them and whole peoples supported them.
6. “Educated people do not believe in ghosts.” He said. “Ah,” I replied, “some
college people do.” “Oh, but they are not educated just because they went to
college,” he answered, “for if they were they would not believe in ghosts.”
7. “There can be no doubt that atomic bombs can poison the atmosphere.
Einstein himself said so.”
8. But Doctor, surely your advice to me to stop smoking cannot be serious, since
I happen to know that you smoke.
9. Socrates is a man; man is a species; therefore Socrates is a species.
10. Every attempt to prove that men are not immortal has failed. No evidence
can be found which shows that men’s souls do not exist after death; hence,
immortality must be true.
Logic Exercises
Exercise #10
Answers
Identify the fallacies committed in the following:
1. Water the plant when thoroughly potted.
2. He:
She:
He:
Dance?
Love to!
Marvelous, that’s better than dancing.
3. Jones was not intoxicated today.
Amphiboly
Emphasis
Significance / Amphiboly
4. Your contention that alcohol is injurious is without merit since you drink.
Ad hominem
5. It has been argued that the Crusades were a noble endeavor, since men of
high purpose founded them and whole peoples supported them. Appeal to
sentiment
6. “Educated people do not believe in ghosts.” He said. “Ah,” I replied, “some
college people do.” “Oh, but they are not educated just because they went to
college,” he answered, “for if they were they would not believe in ghosts.”
Begging the question
7. “There can be no doubt that atomic bombs can poison the atmosphere.
Einstein himself said so.”
Appeal to authority
8. But Doctor, surely your advice to me to stop smoking cannot be serious, since
I happen to know that you smoke.
Ad hominem
9. Socrates is a man; man is a species; therefore Socrates is a species.
Equivocation
10. Every attempt to prove that men are not immortal has failed. No evidence
can be found which shows that men’s souls do not exist after death; hence,
immortality must be true.
Argument from ignorance
(Ad Ignoratium)