1. No ducks waltz.

No officers ever decline to waltz.

All my poultry are ducks.

My poultry are not officers.

2. No experienced person is incompetent.

Jenkins is always blundering.

No competent person is always blundering.

Jenkins is inexperienced.

3. No terriers wander among the signs of the zodiac.

Nothing that does not wander among the signs of the zodiac is a comet.

Nothing but a terrier has a curly tail.

No comet has a curly tail.

4. All hummingbirds are richly colored.

No large birds live on honey.

Birds that do not live on honey are dull in color.

All hummingbirds are small.

5. All unripe fruit is unwholesome.

All these apples are wholesome.

No fruit grown in the shade is ripe.

These apples were grown in the sun.

6. All my sons are slim.

No child of mine is healthy who takes no exercise.

All gluttons who are children of mine are fat.

No daughter of mine takes any exercise.

All gluttons who are children of mine are unhealthy.

7. The only books in this library that I do not recommend for reading are unhealthy in tone.

The bound books are all well written.

All the romances are healthy in tone.

I do not recommend you to read any of the unbound books.

All the romances in this library are well written.

8. No interesting poems are unpopular among people of real taste.

No modern poetry is free from affectation.

All your poems are on the subject of soap bubbles.

No affected poetry is popular among people of real taste.

No ancient poem is on the subject of soap bubbles.

All your poems are uninteresting.

9. All writers who understand human nature are clever.

No one is a true poet unless he can stir the hearts of men.

Shakespeare wrote Hamlet.

No writer who does not understand human nature can stir the hearts of men.

None but a true poet could have written Hamlet.

Shakespeare was clever.

10. I trust every animal that belongs to me.

Dogs gnaw bones.

I admit no animals into my study unless they beg when told to do so.

All the animals in the yard are mine.

I admit every animal that I trust into my study.

The only animals that are really willing to beg when told to do so are dogs.

All the animals in the yard gnaw bones.

The following sorites are taken from Lewis Carroll's Symbolic Logic. All are valid. Rewrite each sorites in standard form, using letters to represent the terms and reducing the number of terms whenever necessary. Then use Venn diagrams or the rules method to prove each one valid.