Counterexample Exercises

      A counter example is an example which runs "counter" to, or against, a general claim.  It is thus a way of criticizing such a claim.  For instance, if someone says, "All the U.S. presidents have been Protestants," one can point to John F Kennedy as a counterexample.  (He was a Catholic.)   A genuine counterexample proves that the claim is false.  Being able to think up good counterexamples is one of the skills a critical thinker needs; it is a way of combating the tendency to make over-hasty generalizations.
Try to give at least one counterexample for each of the claims below.  If you can't give a counterexample for a claim, say so and try to say why.

1) All birds fly.

2) Trees lose their leaves every fall.

3) A German is a person who lives in Germany.

4) All unmarried men are bachelors.

5) In our fast-changing society, the only way to stay informed is to watch the TV news every night.

6) Everything that has color has shape.

7) Everything that has shape has size.

8)   It is always right to tell the truth.

9) It is never right to tell a lie.

10) No nation should ever interfere in the internal affairs of another nation.

11) There is no censorship in the United States.

12) Unlike some countries, the United States never uses terrorism as an instrument of policy.

13) The only legitimate reason for the government to restrict people's liberty is to prevent them from harming others; otherwise people should be free to do as they see fit.