This is a fun logic puzzle from one of Ian Stewart’s many math collections.  I discovered that the problem actually is basically one of Lewis Carroll’s examples from an 1896 book:

1. The only animals in this house are cats.
2. Every animal that loves to gaze at the moon is suitable for a pet.
3. When I detest an animal, I avoid it.
4. No animals are meat-eaters, unless they prowl by night.
5. No cat fails to kill mice.
6. No Animals ever take to me, except those in this house.
7. Kangaroos are not suitable for pets.
8. Only meat-eaters kill mice.
9. I detest animals that do not take to me.
10. Animals that prowl at night love to gaze at the moon.

If all these statements are correct, do I avoid kangaroos, or not?

Answer.

See Do I Avoid Kangaroos? for solutions.