2009-06-01

Ill Logic

Bengt is feeling ill, and is lying in his bed playing around with ternary logic, modal logic, and some other things that he's not sure about the proper terms for.
Given these premises:
  • All donks are ganks.
  • Every gank was created by another (older) gank.
  • Binks are more likely to be donks (in other words, there is a higher fraction of donks among binks than among non-binks).

Evaluate the following statements as definitely true, definitely false, or unknown.
  1. Donks are more likely to be binks.
  2. Some ganks are donks.
  3. Some things are not donks.
  4. There was a first gank.
  5. There is an oldest gank.
  6. If some things, but not all, are binks, and there are no ganks, then some donks are not ganks after all.
  7. If all things are binks, then there is at least one donk.
  8. If all things are binks, and there are some things that are not ganks, then there is at least one donk.