1. Whatever produces oxygen supports human life.

Rain forests produce oxygen.

Nothing that supports human life should be destroyed.

Rain forests should not be destroyed.

2. No restrictive trade policies fail to invite retaliation.

Trade wars threaten our standard of living.

Some Chinese trade policies are restrictive.

Policies that invite retaliation lead to a trade war.

Some Chinese trade policies threaten our standard of living.

3. Anything that poisons drinking water causes disease and death.

Chemicals percolating through the soil contaminate aquifers.

Dumped chemicals percolate through the soil.

Whatever contaminates aquifers poisons drinking water.

Dumped chemicals cause disease and death.

4. Nothing that is brittle is ductile.

Superconductors are all ceramics.

Only ductile things can be pulled into wires.

Ceramics are brittle.

Superconductors cannot be pulled into wires.

5. Some college students purchase their term papers.

Any cheat is expelled from college.

No one will achieve his career goals who is expelled.

No one who purchases term papers is other than a cheat.

Some college students will not achieve their career goals.

6. Creation science does not favor the teaching of evolution.

Nothing should be taught that frustrates the understanding of life.

Whatever opposes the teaching of evolution impedes the learning of biology.

Anything that enhances the understanding of life fosters the learning of biology.

Creation science should not be taught.

7. Whoever gives birth to crack babies increases future crime rates.

Some pregnant women use crack.

None but criminals increase future crime rates.

Pregnant crack users never give birth to anything but crack babies.

Some pregnant women are criminals.

8. Whatever retards population growth increases food availability.

Anything that prevents starvation enhances life.

Birth-control measures never accelerate population growth.

Anything that enhances life should be encouraged.

Whatever increases food availability prevents starvation.

Birth-control measures should not be discouraged.

9. A few countries allow ivory trading.

Whatever country resists elephant killing discourages poachers.

Any country that allows ivory trading encourages poachers.

No country that promotes the extinction of elephants should escape the condemnation of the civilized world.

Any country that supports elephant killing promotes the extinction of elephants.

A few countries should be condemned by the civilized world.

10. Anything that promotes skin cancer causes death.

Whatever preserves the ozone layer prevents the release of CFCs.

Nothing that resists skin cancer increases UV radiation.

Anything that destroys the ozone layer increases UV radiation.

There are packaging materials that release CFCs.

Nothing that causes death should be legal.

Some packaging materials should be illegal.

The following sorites 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.