Standard Categorical Form And Ven Diagram
I. Use Venn diagrams to test the validity of the following arguments.
1. No sharks are pets, since no barracuda are pets, and no sharks are barracuda.
2. No farmers are city dwellers. Hence, since all city dwellers are urbanites, no urbanites
3. All curmudgeons are pessimists. All pessimists are cynics. So, some cynics are
4. Some bankers are vegetarians. No anarchists are bankers. So, some anarchists are not
5. No beach bums are workaholics. Some beach bums are rollerbladers. So, some
rollerbladers are not workaholics.
6. All violinists are musicians. Therefore, since some bookworms are violinists, some
bookworms are musicians.
7. No poker players are early risers. Some firefighters are early risers. So, some
firefighters are not poker players.
8. Some dot-com millionaires are philanthropists. All philanthropists are altruists. Hence,
some altruists are dot-com millionaires.
9. Some telemarketers are Methodists. Some Methodists are Democrats. So, some
Democrats are telemarketers.
10. No Fords are Pontiacs. All Escorts are Fords. So, some Escorts are not Pontiacs.
11. No mockingbirds are cardinals. Some cardinals are songbirds. So, some songbirds are
12. Page 249All ecologists are environmentalists. Hence, because all ecologists are
wilderness lovers, all wilderness lovers are environmentalists.
13. No landlubbers are sailors. Some sailors are not pirates. So, some pirates are not
14. All cats are carnivores. All tigers are cats. So, all tigers are carnivores.
15. All sound arguments are valid arguments. Therefore, because some sound arguments
are mathematical arguments, some mathematical arguments are not valid arguments.
16. No fish are reptiles. All trout are fish. So, some trout are not reptiles.
17. Some dreamers are not romantics, because some idealists are not romantics, and all
idealists are dreamers.
18. Some stockbrokers are couch potatoes. Hence, because all stockbrokers are e-traders,
some e-traders are couch potatoes.
19. Some butchers are not bakers. No butchers are candlestick makers. Therefore, some
candlestick makers are not bakers.
20. All meteorologists are forecasters. Hence, because some forecasters are psychics,
some psychics are meteorologists.
II. Translate the following into standard categorical form. Then use Venn diagrams to test the
arguments for validity.
1. No one who is a Nobel Prize winner is a rock star. A number of astrophysicists are
Nobel Prize winners. Therefore, a number of astrophysicists are not rock stars.
2. Many philosophers are determinists. Anyone who is a fatalist is a determinist. So,
many fatalists are philosophers.
3. If anything is a maple, then it's a tree. Hence, because nothing that is a bush is a tree,
nothing that is a bush is a maple.
4. Everybody who is a liberal is a big spender. Therefore, because Senator Crumley is a
big spender, Senator Crumley is a liberal.
5. Many tarot readers are lottery players. Every tarot reader is a fraud. So, many frauds
are not lottery players.
6. Only poems are sonnets. No mathematical treatise is a poem. Therefore, no
mathematical treatise is a sonnet.
7. At least one lawyer is not a golfer. Only persons who have attended law school are
lawyers. So, at least one person who has attended law school is not a golfer.
8. No one who is a cardsharp is a psychic. Someone is a cardsharp only if he is a poker
player. Therefore, some poker players are not psychics.
9. Whatever is a fish is a nonmammal. Each pickerel is a fish. So, no pickerel is a
10. Only social scientists are political scientists. Many political scientists are persons who
favor campaign finance reform. Accordingly, many persons who favor campaign finance
reform are social scientists.
11. Egoists are not humanitarians. Not a single humanitarian is a sweatshop owner. So, not
a single sweatshop owner is an egoist.
12. There are e-mail messages that are not spell-checked. There are interoffice memos that
are e-mail messages. Therefore, there are interoffice memos that are not spell-checked.
13. Page 250Every tax evader is a lawbreaker. Hence, because no one who is a lawbreaker
is a model citizen, no one who is a model citizen is a tax evader.
14. If anything is a truck, then it is not a car. There are Mazdas that are trucks. It follows
that there are Mazdas that are not cars.
15. Any dog is furry. Lassie is a dog. So, Lassie is furry.
16. Not every lie is immoral, for no harmless acts are immoral and some lies are harmless.
17. Mystics are always religious. At least one religious person is not greedy.
Consequently, at least one mystic is not greedy.
18. Every person who drinks and drives is an irresponsible person. Not every person who
talks on a car phone is an irresponsible person. Hence, not every person who talks on a car
phone is a person who drinks and drives.
19. Anyone who eats pizza every night is at risk for heart disease. Some people who are at
risk for heart disease are cab drivers. So, some cab drivers are people who eat pizza every