HZT 4U Syllogism Exercises
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Syllogism Exercise 1

1. No doctors are enthusiastic
You are enthusiastic.

2. No old rabbits are greedy.
All black rabbits are greedy.

3. Some eggs are hard-boiled.
No eggs are uncrackable.

4. Some buns are rich.
All buns are nice.

5. All soldiers march well.
Some babies are not soldiers.

6. Some tests are not pleasant.
All unpleasant things need to be avoided.

7. No men are graceful.
Some women are ungraceful.

8. No fleas are nice.
Some flies are not fleas.

9. No bowlers have short thumbs.
Some people are not bowlers.

10. Sadam Hussein is not a devil
Some devils should be exorcised.

11. Bill Clinton is a popular president.
Popular presidents should be honest.

12. Some Olympians go faster, higher and stronger.
No Olympians should ever cheat.

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Syllogism Exercise 2

1. Magicians walk through walls
Some skeptics are not magicians.

2. No babies are intolerant.
All diaper-wearers are babies.

3. Some modern songs are cacophonic.
All songs by Meatloaf are cacophonic.

4. A stitch in time saves nine.
All that saves nine should be welcome.

5. No old birds are unscientific.
Some teachers are unscientific.

6. Bridges are not made of paper.
Some bridges are dangerous.

7. Elderly ladies are talkative.
Blue-rinsed ladies are talkative.

8. All wolves are hungry.
Some wolves do not eat sushi.

9. Some perfume reeks badly.
All perfume is expensive.

10. Caterpillars turn into strange things.
Some strange things are seen on Yonge Street.

11. Some watermelons are juicy.
No watermelons are purple.

12. There are no saints in hell.
Some saints have a shiny halo.

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Syllogism Exercise 3

1. Downhill skiers are on the edge.
Some downhill skiers are reckless.

2. Kevin Overland is a smooth skater.
Some smooth skaters slip and slide.

3. Myriam Bedard is a straight shooter.
Straight shooters are sometimes disappointed.

4. No Olympic flags are purple and gold.
Some skating costumes are purple and gold.

5. Some figure skaters cut a fine figure.
Elvis Stoiko cuts a fine figure.

6. Some Sumo wrestlers shout, “Where’s the beef?”
No Sumo wrestlers should wear tutus.

7. All luge riders look like stuffed sausages.
Some luge riders don’t fit into their tight suits.

8. Women’s hockey is not ready for the Olympics.
Some things not ready for the Olympics are boring to watch.

9. Some free-style skiers have vertigo.
All who have vertigo fall head over heels.

10. Jean-Luc Brassard is a flying machine.
Some flying machines crash and burn.

11. Olympic ticket prices are sky-high.
Nothing sky-high should be supported.

12. All prostitutes were removed from Nagano.
Some prostitutes are an embarrassment.

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Syllogism Exercise 4

1. Little Red Riding Hood took fruit and mineral water to her grandmother.
Some who take fruit and mineral water to their grandmother are generous.

2. Some forests are dark and dangerous places.
Dark and dangerous places are filled with Freudian imagery.

3. Some baskets are filled with healthful snacks.
All baskets are coveted by big bad wolves.

4. All grandmas have very big noses.
Some wolves are not grandmas.

5. Some Cinderellas are treated very cruelly.
All who are treated cruelly are marginalized as unpaid workers.

6. Goldilocks was a melanin-impoverished young wommon.
Some melanin-impoverished young wommon need to avoid the sun.

7. Some jealous queens chemically alter their apples.
No jealous queens are the fairest of them all.

8. Some frogs are really princes.
No real princes smell badly.

9. Some giants smell the blood of an English person.
No beanstalk choppers are giants.

10. Some nasty tunes are played by the Pied Piper
No nasty tunes are easy to resist.

11. Some princesses are bothered by peas.
The Jolly Green Giant is not a princess.

12. All tortoises have a low metabolism.
No hares have a low metabolism.

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Syllogism Practice

1. Skate boarders have messy clothes.
Some who do no have messy clothes are untalented.

2. Some short people get picked on.
Only sensitive people are short.

3. Some unemployed men are lazy.
No working men are unemployed.

4. Some birds are flighty.
No helicopters are flighty.

5. Some apples are juicy.
No apples are purple.

6. Some firefighters are fit.
All firefighters are courageous.

7. All hospital workers are overworked.
Some librarians are not hospital workers.

8. Some grapes are not good for wine-making.
What is not good for wine-making should be vinegar.

9. No singers hit high notes.
Some birds hit high notes.

10. No waves are silent.
Some evenings are silent.

11. No tenors like sore throats.
Some people are not tenors.

12. No cousins should get married.
Some men should not get married.

13. No pumas are putrid.
Some plums are putrid.

14. No spring birds are on time.
Some spring birds are amorous.

15. Some who play golf are duffers.
None but old ladies play golf.

16. All actors have inflated egos.
Keanu Reeves is no actor.

17. Downhill skiers never show fear.
Some pigeon-toed people are not downhill skiers.

18. All opera singers are two hundred pounds.
Karen Kain is no opera singer.

19. He never sings in the shower.
Singing in the shower is a normal behaviour.

20. No trout are striped and polka-dotted.
Some trout are devious swimmers.

21. All elephants are naturally patient.
Some pachyderms are not elephants.

22. All detergents are not environmentally friendly.
All things not environmentally friendly should be banned.

23. Some films are not an insult to one's intelligence.
No good novels are an insult to one's intelligence.

24. All chocolate is not fattening.
Some chocolates are expensive.

25. Some mud does no stick to your boots.
All mud sticks in your throat.

26. Some oil changes are major car repairs.
Engine burnouts are not oil changes.

27. All female presidents cause a shake-up.
Some blenders cause a shake-up.

28. Some who lose credibility are finished.
All faith-healers have lost credibility.

29. Every reckless driver should be jailed.
All drunk drivers are reckless.

30. Some bands are too loud.
Bands should provide earplugs.

31. What has not worked should be scrapped.
None of his solutions worked.

32. Some astronauts are beyond brave.
All policemen are beyond brave.

33. Brothers in arms are not in dire straits.
All talking heads are brothers in arms.

34. A painting reaches our finer instincts.
Paint-by-number pictures are not paintings.

35. Some bananas are very green.
What is very green should be left to ripen.

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Extra Practice (Exercise 5)

Slave to the Syllogism… 

1. Computers do not make life easier.
Secretaries make life easier.

2. Some comics use the f-word.
Nuns are not comics.

3. Coffee is the nectar of the gods. (mmm… coffee…)
Some godly nectar is addictive.

4. No smoking on school property.
The “rail” is school property.

5. 60s bands rock.
Some who rock are stones.

6. Only the good die young.
Some who are not at fault die young.

7. Sir James Dunn leads the way.
Only Sir James Dunns are known as flagships.

8. Love is a four letter word.
Four letter words are not always profane.

9. Logic is fun.
Some fun is hard work.

10. Some greyhounds go fast.
No greyhounds are puck hungry.

11. Santa wears red.
Some who wear red are not Satan.

12. All who live long get old.
Some who live long prosper.

13. Drawing Venns is tiresome.
Some boring things are not tiresome.

14. Only cats are tigers.
Some cats are not cool.

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Multiple Premise Syllogisms (Lewis Carroll calls them "sorites" arguments...)

While the first two examples below can be proven easily using Venn diagrams, Lewis Carroll came up with his own method of solving these multi-premise conundrums.  He used bilateral and trilateral diagrams to solve them.  (click here if you're really curious...)

Using his diagrams, it's possible to solve things that we got no conclusions for when we used Venn diagrams (which is probably why not all philosophers agree with his paradoxes.)    As discussed in class, sometimes in order to get a solution, we need to make inferences for opposite terms.  For example, in the third example below, "boarders" would be opposite to "day boys"; thus, when trying to find like terms, day boys could become "not boarders" (or "boarders" would become "not day boys").  Carroll uses letters to represent terms like we did with Venns.  In conjunction with his bi- and trilateral diagrams, boarders and not boarders would become a and a'.

See if you can come up with conclusions to the sorites.  I do not expect you to "get" this.  I'm not even sure I do.  It's merely for interest and to challenge your logical and deductive powers.  Don't abuse them...

Ooh, your powers of deduction are exceptional.  I can't allow you to waste them here when there are so many crimes going unsolved at this very moment.  

Go! Go, for the good of the city.


Multiple Premise Syllogisms (Sorites)

1. No ducks waltz.
No officers ever decline to waltz.
All my poultry are ducks.

2. Nobody, who really appreciates Beethoven, fails to keep silence while the Moonlight-Sonata is being played.
Guinea-pigs are hopelessly ignorant of music.
No one, who is hopelessly ignorant of music, ever keeps silence while the Moonlight-Sonata is being played.

3. No boys under 12 are admitted to this school as boarders.
All the industrious boys have red hair.
None of the day boys learn Greek.
None but those under 12 are idle.

4. Promise-breakers are untrustworthy.
Wine drinkers are very communicative.
A person who keeps his promise is honest.
No teetotalers are pawnbrokers.
One can always trust a very communicative person.

5. I trust every animal that belongs to me.
Dogs gnaw bones.
I admit no animals to my house unless they beg.
All the animals in the yard are mine.
The only animals willing to beg are dogs.
I admit every animal into my house that I trust.

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Venn Intro Universals Particulars Exercises Answers


This page last updated April 20, 2004 by G. Flood